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程序代写案例-2022S1
时间：2022-06-14
!
2022S1
Tutor: Mandy
FINC3017
Investment and Portfolio Management
Final Review & Practice Questions
Ø Final Exam Details
Ø 复习建议
ü Lecture & Weekly 相关知识点、概念巩固
ü 至少一遍 Tutorial 题目(解题思路)
ü 独立做题 & 讲解
Final Exam
Exam Date 13:00PM, 16 June 2022 (Sydney Time)
Exam Duration 1 hour and 40 minutes long, including 10 min reading time
Exam Type Open book exam*
Question Type and weight • ~30%: Multiple Choice Questions
• ~70%: Short answer questions (numerical)
Coverage Covers the entire unit but with less emphasis on portfolio theory
*Materials permitted: Matlab, Python, handheld calculator, computer's calculator, a hard copy of a formula sheet and statistical table,
Microsoft Excel, multiple sheets of blank scratch paper and a pen/pencil. Online resources (including Unit of Study Canvas resources,
eBooks and internet search), locally saved notes on the computer and paper-based resources (including printed/handwritten notes and
textbooks). Be mindful that you may not finish the exam within the permitted time if you frequently search for resources to help you
answer the questions.
Open-book exams do not permit the use of third party communication or collaboration apps or websites. Access to any such app or
website is strictly prohibited during your exam and is a serious academic integrity breach.
!
Ø Weekly Contents
Ø Study Guide & Review
² Asset classes and financial instruments
1. Different types of financial instruments
l Equity: Common stock, preferred stock
l Debt: T-bills, T-notes, T-bonds, Corporate bonds, International bonds
l Derivatives: Option (call and put), Future, Forward, Swap
2. How securities are issued and traded
l Primary market V.S. Secondary market
ü Primary market(一级市场): 发行市场，证券首次出售给公众的市场。
ü Secondary market(二级市场): 已发行的有价证券交易、买卖流通的场所。
l IPO/Initial public offering: the first issue of shares to the general public.
l Trading markets:
ü Direct search markets: Buyers and sellers seek each other directly. (the least organized)
ü Brokered markets: Brokers search out buyers and sellers. (不具有买卖资产的所有权)
ü Dealer markets: Dealer purchase assets for their own accounts, and later sell them for a
profit from their inventory.
ü Auction markets: Traders converge at one place to trade.
FINC3017 Weekly Topic
Basic Concepts
Week 1. Introduction • 资产、金融工具的分类、特点
• Buying on margin & short selling理解与
计算Week 2. Asset Classes and Financial Instruments
Portfolio Theory
Week 3. Risk Return Relation and Portfolio Analysis • 相关概念的理解、辨析
• 两类模型的特点、异同对比
（大约2-3题）Week 4. Markowitz Model
Week 5. Single Index Model (Implementing Portfolio Theory)
CAPM & Anomalies
Week 6. CAPM • 相关概念的理解
• 检验的判断、意义
• Anomalies种类和结论Week 7. Testing the CAPM
Week 8. Anomalies
Performance Evaluation Week 9. Performance Evaluation • 定量计算
Asset Pricing Week 10. Asset Pricing Theory • 定性理解
• 定量计算
Current Research
Week 11. Return Predictability • 定性理解
• 可能有简单计算
Week 12. Volatility
!
3. Buying on margin and short selling
相关概念回顾：
ü Initial margin：初始保证金，在建立初始头寸时，投资者需要支付的自有资金.
ü Maintenance margin:需要维持保证金账户自有现金的最低限额.
ü Margin call: 当账户中自有金额低于最低要求时，会触发 margin call 要求补充自有
金额.
l Buying on margin: assume the price will go up and borrow money to purchase the securities.
* Asset (stock value) = Equity (own money) + Liability (borrowed money, 固定)
* Equity in account = stock value – money borrowed + additional funds
* Stock value (market value, 变动)= #number of shares x market price
ü Margin = Equity in AccountStock value = Stock value − borrowed moneyStock value
ü !"#$%& $( )**+#(%,-./#0 +1 2%+*3, = #(#5607 +1 28.702 × 5.730% :7$*0 ; 6+77+<0= 5+(0&#(#5607 +1 28.702 × 5.730% :7$*0 <
l Short selling: assume price will drop and borrow securities to sell, later buy back to cover.
* Asset (Total margin account) = Equity (own money) + Liability (stock owed)
* Initial Equity = Initial margin rate x Initial market value of stock
* (Short Sale) Equity = Total margin account(固定) – Market value of stock
ü = !"#$%&-./#0 +1 2%+*3 = >+%./ 5.7?$( .**+#(% ; -./#0 +1 2%+*3-./#0 +1 2%+*3
ü !"#$%& $( )**+#(%,-./#0 +1 2%+*3, = >+%./ 5.7?$( .**+#(% ; #(#5607 +1 28.702 × 5.730% :7$*0#(#5607 +1 28.702 × 5.730% :7$*0 <
à Receive margin call when: Equity <= Maintenance margin X Market Value of Stock
ASSET LIABILITY
Stock value Equity (own money)
Liability (borrowed money)
ASSET LIABILITY
Total margin account Equity (Deposited own money ± fluctuation)
Liability (market value of short position in securities)
!
² Portfolio theory
1. Risk-return
l Return measurement：
ü Simple net return (HPR) – Single period: 8 = 9!:;!<9!"#9!"# = 9!:;!9!"# − 1
ü Simple gross return – Single period: 1 + 8
ü Asset gross return – Multiple period: 1 + 8() = (1 + 8)(1 + 8<=)(1 + 8<>)… (1 + 8ü Log return – Single period: 8 = (1 + 8) = 0 88<=1 = 8 − 8<=
ü Log return – Multiple period: 8() = log (1 + 8()) = 6(1 + 8)(1 + 8<=)… (1 + 8
l Average Return：
ü Arithmetic average return(算术平均)
ü Geometric average return (几何平均) (1 + @) = (1 + =)(1 + >)… (1 + A)=A
ü Dollar weighted average return (满足下式的 internal rate of return) BCDEFG = FH8DEFG
l Risk measurement：
ü Variance: average/expected value of squared deviations from mean.
ü Standard deviation (): square root of variance, often called volatility.
ü Sharpe Ratio ℎ = ̅B − DB
l Conversion of Annualizing return, Variances, Volatility(年化转换的计算)
!
2. Mean variance analysis
l Risk-return trade-off: 既定风险下的最大收益或既定收益下的最小风险.
l Portfolio return and variance: I = D BBCBJ= I> = D B>B>CBJ= +DDBK(BK)KBLK
l Investment opportunity set
ü 2-Risky Asset: Investment opportunity set is the entire curve (下图左)
ü More than 2: the entire area inside the hyperbola. (下图右)
l Efficient portfolios: portfolios on efficient frontier.
l Efficient frontier: the upper branch of the curve.
l Minimum variance portfolio: the left-most
portfolio.
l Capital market line (CML):
ü Special CAL which is tangent to the efficient
frontier.
ü Highest Sharpe ratio/slope
ü Efficient frontier for portfolios combined
Multiple Risky Assets+ Risk-free Asset
l Tangency portfolio
l Effect of correlation (2-asset): There are benefits to diversification whenever asset returns are
less than perfectly positively correlated -as ρ becomes more negative, more diversification
benefits. (两类资产负相关越强，能达到的分散化优势越强)
l The risk of a large portfolio: The risk of a portfolio with many assets is largely determined by
average covariance risk - correlation/covariance risk can change very quickly.
T-bill
Stock
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00%
Rp
!
3. Markowitz and Single Index Model
l SIM Formula:
ri,t = ai + βimt + ei,t
s : expected return related to firm-specific factor. (个股相关的预期收益率)
s mt: expected return related to market. (市场相关的预期收益率)
s ,t : unexpected return (firm-specific) or residual. (unexpected event 相关的收益率)
l Variance
σi2 = βi2σm2 + σ2(ei)
s βi2σm2: 系统性风险
s σ2(ei): 非系统性风险/公司特有风险
l Covariance Matrix
l Markowitz V.S. SIM
Markowitz Mean-Variance Model Single Index Model
Number of Input Data
(初始需要的数据量)
• N return estimates
• N Variance estimates
• (N2 – N)/2 Covariance estimates
Total = (N2 + 3N)/2
• N α estimates
• N β estimates
• N Variance estimates
• 1 estimate of market return
• 1 estimate of market variance
Total = 3N + 2
Assumptions of return
(假设条件)
• No assumption on return generating process.
• Parameter values obtained by calculating
sample estimates from historical data.
• SIM makes assumptions about the return generating
process.
• The parameters are obtained through the imposed
assumption on data generating process.
Computation issue • More data involved as n increases à difficult to
calculation.
• Easier than Markowitz model.
• Vastly reduced the number of estimates. ! and Covariance Matrix • Estimated from historical data • Calculated based on the estimates obtained from
regression model.
!
² CAPM
1. The link between portfolio theory and the CAPM
l Portfolio theory analyses how investors form their portfolios given asset risk and return
characteristic. (risk-return trade-off)
l CAPM shows how risky assets are priced. It explains:
ü What is tangency portfolio?
ü How does investors’ asset demand determine the relation between assets’ risk and return
in an equilibrium? (重要思想/机制：asset demand = asset supply)
2. Implications of the CAPM (important concepts such as alpha, beta, and SML)
l CAPM Assumption: perfect capital market
l CAPM Formula: [B] = D + B 6[M]−D7 or [B] − D = B ([M] − D) B = (B , M)M>
l Predictions:
ü the tangency portfolio is the market portfolio
ü the expected return on any risky asset E[ri] is given by the above formula
ü the market risk premium can be represented by: [M] − D = ̅M>
l Implications:
1) In equilibrium, the market portfolio is the unique mean-variance efficient tangency portfolio,
and all investors should hold the market portfolio. No one can outperform/beat the market
in the long run, thus a passive strategy is efficient.
2) CAPM equation shows the risk-return relationship (can plot as SMLà return-beta).
3) It implied security risk is related to beta and market risk premium, and only systematic risk
(market risk) will be rewarded. High beta securities are more risky à perform badly when
the market goes down.
4) High beta security should earn high return.
5) It can be used to calculate discount rate/required rate of return/opportunity cost of capital.
6) It provides a benchmark rate of return (SML) for evaluate investment performance, and a
method for performance evaluation of fund/portfolio managers. à using alpha and pursue
positive alpha.
l Alpha/α: the abnormal rate of return on a security in excess of what would be predicted by the
CAPM. (actual expected return – fair expected return via CAPM)
l SML (Security Market Line): Graphs individual asset risk premiums as a function of asset
risk/ asset’s beta.
!
3. Testing the CAPM
l Portfolio sorts: 基于特定特征分类分组排序
l Regression-based approaches
ü Time series regression
回归方程：by running OLS time-series regressions: 8NB = B + B8 + 8B, t = 1,2,3, …, T
s 8NB: the excess return of asset i;
s 8: the excess return of the market;
s Asset can be individual stock or portfolios
检验目标：B = 0；B显著不为 0.
ü Cross-section regression
回归方程: by running a cross-sectional regression of average excess returns on the betas: (8NB) = O + B + B, i = 1,2,3, …, N
检验目标: λ0 = 0; λ = market risk premium > 0.
ü Fama-MacBeth regression
基本回归方程：running a cross-sectional regression at each time period 8NB = O,8 + 8B + B8, t = 1,2,3, … T, for each t
检验目标: SO = 0；S8 = market risk premium
l t-test 判断方法
[当原假设为：检验参数 = 0]
1) t-stat (越大越拒绝)
t-stat > t 临界值 à 落入拒绝域，拒绝原假设，则对应参数显著不为 0.
t-stat < t 临界值 à 不能拒绝原假设，则对应参数显著为 0.
注：t 临界值可以粗略取值为 1.96 或 2.
2) p-value (越小越拒绝)
p-value < significant level (5%) à 拒绝原假设，则对应参数显著不为 0.
p-value > significant level (5%) à 不能拒绝原假设，则对应参数显著为 0.
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -0.0011341 0.006276525 -0.1806863 0.85724367 -0.0136979 0.01142975
Mkt - rf 0.97007904 0.189292106 5.12477282 3.5697E-06 0.59116972 1.34898836
!
4. Anomalies
l Anomalies: the stylized facts that stocks with certain characteristics tend to outperform relative
to others. (可理解为通过实际观测到的数据结果与理论模型得出的结果不同或相违背)
ü Size Effect/ Small-firm Effect: small stocks outperform large stocks.
ü Value Effect (Book-to-market ratio): stocks with high book-to-market ratios (value stock)
outperform those with low book-to-market ratios(growth stock).
ü Profitability anomaly: companies that are more profitable outperform those that are less
profitable.
ü Investment anomaly: companies that do more investments underperform those that do less
investments (e.g. R&D expenditure).
ü Momentum anomaly: Winner stocks outperform loser stocks. (good or bad recent
performance of particular stocks continues over time)
l Interpretations of anomalies
ü Those return patterns/anomalies are due to the mispricing.
ü Nothing wrong with the return pattern, just the pricing model we use is wrong/ cannot
explain the return pattern so well à we may need to consider more realistic model.
² Performance Evaluation
1. Average returns (simple average, time-weighted average, and dollar weighted average)
参考 Portfolio theory
2. Risk adjusted performance measure: Sharpe ratio, M2 , Treynor ratio, and alpha
Formula Implication/意义 Other characteristics
Sharpe ratio
= ̅! − ̅"!
Measurement of excess return per unit
of total risk.
- Dose not rely on particular
asset pricing model.
- May be manipulated.
- Numerical value is difficult
to interpret. # = $∗ − & = (! − &) × &
Comparison of the return between
adjusted portfolio’s return and the
market index, as they have the same
standard deviation.
- Adjust the portfolio(P)
standard deviation to match
with the passive market index
à P*
B = CC = C∗
Treynor
ratio
= ̅! − ̅"!
Measurement of excess return per unit
of systematic risk.
- Needs to estimate beta.
- Appropriateness of CAPM.
Jensen’s
alpha
$ = ̅! − [̅" + !(̅& − ̅")] Measurement of the average return on the portfolio over and above that
predicted by the CAPM.
Alpha is model dependent.
!
² Asset pricing
1. State space model (important concepts such as AD securities and state prices)
l Arrow-Debreu Securities (ADS): it will pay off $1 if state of nature s occurs next period and
zero otherwise. For example：
s=1 s=2 s=3
⎣⎢⎢
⎢⎢⎡
100...0⎦⎥⎥
⎥⎥⎤
⎣⎢⎢
⎢⎢⎡
010...0⎦⎥⎥
⎥⎥⎤
⎣⎢⎢
⎢⎢⎡
001...0⎦⎥⎥
⎥⎥⎤
l State prices/Ws :为当前时点上述 AD Security 的价格，且满足 0< Ws <1.
l Risky asset with random pay off Y can be represented as:
Y =
⎣⎢⎢
⎢⎢⎡
=>Q...R ⎦⎥⎥
⎥⎥⎤
也可通过 AD Securities 表示为：Y = = ⎣⎢⎢
⎢⎢⎡
100...0⎦⎥⎥
⎥⎥⎤ + > ⎣⎢⎢
⎢⎢⎡
010...0⎦⎥⎥
⎥⎥⎤ + Q ⎣⎢⎢
⎢⎢⎡
001...0⎦⎥⎥
⎥⎥⎤+. . . +R ⎣⎢⎢
⎢⎢⎡
000...1⎦⎥⎥
⎥⎥⎤
l State Prices and SDF
à 引入 Physical Probability R = DR RR RR= = DR R RR= = (R R)
l Inferring State Prices from Option Prices (大概率会考计算, 结合/融合上述知识点)
!
2. Link between state prices and risk neutral probabilities
l Risk Neutral Probability 标记为 _R, 且满足 0< _R <1，∑ _RS= = 1， 可表示为： _R = R = R∑ RR=
3. Consumption based asset pricing and the fundamental equation of asset pricing E(MR)=1.
l Fundamental Asset Pricing Equation = [:( + ,:)]
à 可简化为：
E(MR)=1
s R 为 Gross return
s 8:=：(基于 Fundamental Equation)
ü intertemporal marginal rate of substitution of the investor/stochastic
discount factor(SDF)/ pricing kernel/ marginal utility.
ü Random variable and always positive.
ü Economic meaning: High 8:= corresponds to low consumption à
marginal utility is high when the level of consumption is low.
s 等式说明 expected discounted return都是相同的，均为 1；即使不同时间、不
同资产的期望收益可能不同(e.g., 8[1 + B,8:=])
à More general case:
s 8:= /SDF 为正，是基于市场上无套利机会的假设.
s Different asset pricing models use different 8:=. (即不同的折现因子)
s 8:= can be expressed as an index for bad times. (M 越高，则说明越能说明是 bad
times 的情形; 可以理解为当消费者处于 bad time，消费水平比较低/low level of
consumption，边际效用就会越高/high marginal utility)
l 各类变形式及 implications
!
4. Consumption model with power utility (the equity risk premium puzzle, the risk-free rate puzzle,
and HJ bound)
l 各类变形式及 implications
l Equity Risk Premium Puzzle
ü Most economists believe risk aversion γ should be less than 10. (但实际观测到的
值非常高，因此相违背)
ü Power utility model can only fit the equity premium if the coefficient of relative risk
aversion is very large.(需要非常大才能满足相应等式)
l Risk-free rate puzzle
依据等式 : rW,X:= = − + ∆8:= − Y$Z%$>
解读：
若非常大，则等式右侧第二项∆8:=也会较高，如果要使无风险利率满足较低水平，
则需要非常大，需要接近或者大于 1；而作为时间折现因子，合理范围是 0 到 1，但
根据实际的数据，则可能需要大于 1，意味着一个较低的甚至是负向的时间偏好率，
不合理，前后矛盾。
l HJ bound
M ≥ EX kr[,X:=l − rW,X:= + B>2B
ü 依据该公式，SDF 对数形式的标准差应该大于等于市场上资产的最大 Sharpe ratio；
ü 市场资产组合的 Sharpe ratio约为 50%；
ü 结合等式：8:= = − ∆8:= à () = (∆8:=), 需要较大的
[由于市场资产组合的 Sharpe ratio约为 50%，因此意味着M要大于等于 50%，而基于
数据(∆8)相较于()非常小，所以需要较大的满足上述等式.]
*Equity risk premium puzzle 另一视角解读: stochastic discount factor implied from the standard
consumption-based asset pricing models is not volatile enough.
!
² Stock Return Predictability
1. Understanding stock return predictability
l Classic view V.S. Modern View
l Forecasting with
ü Past return
ü Technical indicators
ü Economic variables (D/P ratio)
2. Empirical evidence and interpretation
l D/P ratio & 相关结论
3. Statistical issues of return predictive regressions (e.g., Stambaugh bias)
l Issue 1_ Overlapping data à Traditional OLS standard error not appropriate (理解对应 3种
解决方法)
l Issue 2_Stambaugh bias: a bias in predictive coefficient in finite sample if predictor is
persistent and its shocks are correlated with returns. (其他影响包括 R2和 t-stat 也会有偏差)
² Volatility
1. Different notions of volatility
l Realised/ historical/ backward looking
l Expected/ Ex-ante/ Forward looking
2. Volatility measurement, modeling, and forecasting (理解如何通过模型预测)
3. Understand the economics of volatility derivatives with a focus on VIX futures
!
Ø Exam Practice Questions
【Week 2】
1. Which of the following is a derivative security?
A. Banker’s Acceptance
B. Cross currency swap
C. Preferred stock
D. Commercial Paper
2. Which of the following belongs to money market securities?
A. 6-month T-bill
B. 8-year Corporate Bond
C. 15-year T-Bond
D. 5-year T-Note
3. A purchase of a new issue of stock takes place
A. in the secondary market
B. in the primary market
C. usually with the assistance of an investment banker
D. in the secondary and primary markets
E. in the primary market and usually with the assistance of an investment banker
4. On which of the following market it is most likely to transfer an asset between the third party and
buyer/seller?
A. Direct search market
B. Brokered market
C. Dealer market
D. Auction market
5. Initial margin requirements are determined by
A. the Securities and Exchange Commission
B. the Federal Reserve System
C. the New York Stock Exchange
D. the Federal Reserve System and the New York Stock Exchange
!
6. Jack purchased COL stock at $14 per share. The stock is currently selling at $17. His gains may be
protected by placing a
A. stop-buy order
B. limit-buy order
C. market order
D. limit-sell order
7. Which of the following orders instructs the broker to buy at the current market price?
A. Limit-buy order
B. Limit-sell order
C. Stop-buy order
D. Market order
【Buying on margin】
8. Tom has $12,000 cash on hand and want to buy shares of Company A at $30 from broker using as little
of his own money as possible. The initial margin requirement is 40% and the maintenance margin is 20%.
Tom can borrow _______ as the maximum amount from the broker. Upon borrowing from the broker,
the total number of shares Tom can buy is _______. Tom will receive a margin call if the stock price
drops lower than _________ per share.
【Short selling】
9. Jason decides to short sell 200 shares of stock A with current market price at $35 per share. The total
proceeds he will get from it is ______. The broker set the initial margin as 60%, then he has to deposit
______ to the margin account. If the maintenance margin is 40%, Jason will receive the margin call if
the price increase to more than ______ per share.
【Week 3】
10. An investor purchased one share of stock for $ 40, then received $3 dividend at the end of the month
and sold it for $45. The simple net return is _____.
11. The returns for stock WOW over the past 4 years were 3%, 8%, -2%, 6% respectively, the arithmetic
average return is _______ and geometric average return is ________. (Round to two decimals)
12. The return and variance of Stock BNP in the past three month was 4% and 1.5% respectively, what’s
the annualised return and variance?
A. 12%; 4.5%
B. 16%; 6%
C. 12%; 3%
D. 16%; 3%
!
13. The daily return and variance of Stock COL was 0.05% and 0.1% respectively, what’s the annualised
return and standard deviation?
A. 18.25%; 36.5%
B. 12.6%; 25.2%
C. 12.6%; 50.20%
D. 18.25%; 60.42%
【Week 4_Markowitz】
14. Following the table below, if the correlation is 0.8, the portfolio return is _______ and standard
deviation is ________. (Please present in percentage format and round to 2 decimals)
Stock Return Variance Weight
A 6% 12% 30%
B 12% 20% 70%
15. An investor has a risk aversion coefficient of 5. The expected return and standard deviation of the optimal
risky portfolio are 15% and 25%, respectively. If the Sharpe ratio of the optimal capital allocation line is
0.48, what is the proportion of the investor’s combined portfolio that should be invested in the risky
portfolio that would maximise their utility?
A. 9.6%
B. 19.1%
C. 33.8%
D. 38.4%
16. Treasury bill pays a 6% rate of return. A risk averse investor __________ invest in a risky portfolio that
pays 12% with a probability of 40% or pays 2% with a probability of 60% because __________.
A. might; she is rewarded a risk premium
B. might; the portfolio offers a higher return than the Treasury bill even though it is risky
C. would not; she is not rewarded with any risk premium
D. would not; the risk premium is too small
E. would not; risk averse investors will always choose the risk-free asset
17. The optimal risky portfolio can be identified by finding _____________.
A. the minimum variance point on the efficient frontier
B. the maximum return point on the efficient frontier
C. the tangency point of the security market line and the efficient frontier
D. the efficient portfolio with the highest Sharpe ratio
!
【Week 5_SIM】
18. Which of the following is not the characteristic of SIM?
A. Impose the assumption on data generating process
B. Reduce the number of parameters to estimate
C. Covariance matrix is calculated with historical data
D. Easier than Markowitz on computation
19. A single-index model uses __________ as a proxy for the systematic risk factor.
A. a market index, such as the S&P 500
B. the current account deficit
C. the growth rate in GNP
D. the unemployment rate.
20. As diversification increases, the firm-specific risk of a portfolio approaches
A. 0.
B. 1.
C. infinity.
D. (n – 1) × n.
21. The index model has been estimated for stocks A and B with the following results:
RA = 0.02 + 0.5RM + eA
RB = 0.01 + 0.8RM + eB
σM = 0.25; σ(eA) = 0.20; σ(eB) = 0.15
The covariance between the returns on stocks A and B is
A. 0.0625
B. 0.0250
C. 0. 2200
D. 0.0380
22. Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope
of the regression line is an estimate of
A. the α of the asset
B. the β of the asset
C. the σ of the asset
D. the δ of the asset
!
23. In single index model, the return on a stock in a particular period will be related to
A. firm-specific events
B. macroeconomic events
C. the error term
D. both firm-specific events and macroeconomic events
24. Assume that stock market returns do not resemble a single-index structure. An investment fund
analyses 120 stocks in order to construct a mean-variance efficient portfolio constrained by 150
investments. They will need to calculate _____________ expected returns and ___________ variances
of returns.
A. 120; 120
B. 120; 14400
C. 14400; 120
D. 14400; 14400
25. An investment fund analyses 125 stocks in order to construct a mean-variance efficient portfolio and
single index model respectively constrained by 125 investments. They will need to calculate
_________ covariances for mean-variance model and _________ variance for single index model.
A. 125; 125
B. 15625; 125
C. 7750; 125
D. 15625; 15625
【Week 6-8_CAPM & Anomalies】
26. Which of the following is on the horizontal axis in a plot of the Security Market Line?
A. Standard deviation
B. Beta
C. Expected return
D. Risk premium
27. According to the CAPM, the market portfolio has a beta of _____ and the intercept of the security
market line is _______. (Y-axis represents the excess return)
A. 0, 0
B. 0, risk-free rate
C. 1, 0
D. 1, risk-free rate
!
28. In the context of the CAPM, the relevant risk is
A. unique risk.
B. systematic risk.
C. standard deviation of returns.
D. variance of returns.
29. According to the CAPM, which of the following is true?
A. The expected return of an asset with beta of zero is zero.
B. The slope of the security market line is the Sharpe ratio of the market portfolio.
C. The X-axis of SML is the standard deviation of the investment asset/portfolio.
D. All else equal, the higher the alpha, the better the investment is.
30. The expected return on market is 7% and the risk-free rate is 3%. The beta of CBA is 1.5. According to
the CAPM, the expected rate of return of CBA is ________.
31. Assume the risk-free rate is 1% and the average investor has a risk-aversion coefficient of A = 3. We
also know the standard deviation of the market portfolio and stock JBH is 15% and 20% respectively.
The JBH has a beta of 0.8. According to the CAPM, the equilibrium value of the market risk premium
is _________, the expected return on the market is _________, and the expected rate of return on JBH
is __________. If the historical return of JBH is 9%, the alpha of JBH is ________.
32. A fund manager has managed a portfolio, which had an average annualized return of 12% with standard
deviation of 8% over the last 5 years, and its estimated beta during the period was 0.6. Suppose over the
sample period, the risk-free rate is 4% and the average return on the market is 11%. What was the
manager’s alpha? Did the manager exhibit positive performance ability according to the CAPM?
A. 2.8%; Yes
B. 3.8%; Yes
C. -3.8%; No
D. -2.8%; No
33. The analyst tries to estimate the following cross-sectional regression of average excess returns of the
various sectors under managed portfolios on their betas and volatilities: ri = λ0 + λ1betai + λ2voli + ei,
according to the CAPM, what should we expect for λ0, λ1, and λ2?
A. 0, 0, 0
B. market return, 0, 0
C. 0, market risk premium, 0
D. 0, 0, market risk premium
!
34. According to the size effect, what would be the best way to construct the trading strategy?
A. long small stock and large stock at the same time
B. long small stock and short large stock
C. short small stock and long large stock
D. short small stock and short large stock at the same time
【Week 9】
35. Jason purchased a share of stock for $20 at the beginning of year 1. At the end of year 1, he received $2
dividend and purchased one more share for $23. At the end of year 2, he received $1 dividend and sold
two shares for $25 each. The geometric average return is _______ and dollar weighted return is ______.
36. Consider the two excess return index models for portfolio A and B, the risk-free rate over the period was
6% and the market’s average return was 14%. (Round results to 4 decimal place)
PORTFOLIO A PORTFOLIO B
Model Estimates 1% + 1.2(rm-rf) 2% + 0.8(rm-rf)
R squared 55% 48%
Residual Standard Deviation 10.3% 19.5%
Standard Deviation of Portfolio 21.6% 24.9%
For Portfolio A, the Sharpe Ratio is ________, the Treynor ratio is ________ and alpha is_________.
For Portfolio B, the Sharpe Ratio is ________, the Treynor ratio is ________ and alpha is_________.
37. A portfolio generates an annual return of 14%, a beta of 1.5, and a standard deviation of 16%. The
market index return is 10% and has a standard deviation of 12%. What is the M2 measure of the portfolio
if the risk-free rate is 2%? What’s the weight in risk-free asset?
A. 4%; 75%
B. 1%; 75%
C. 4%; 25%
D. 1%; 25%
!
【Week 10】
38. Suppose the state of nature is summarized by the value of the market portfolio which has a discrete
probability distribution with possible values of: [$1, $2, $3, $4, $5]. Call options on the market portfolio
with different strike prices are available and their prices are given below:
1) Using the above information, calculate the price of the Arrow-Debreu security for each state.
2) What is the risk neutral probability of the state where the value of the market portfolio is equal to $3?
3) What is the price of a put option with a strike price of $5?
39. Consider a single period economy which can enter into one of two possible states (A, B). Each of these
states occurs with equal probability. In state A, a risky asset will have a net return of 0.5, while in state
B it will have a net return of -0.2. There is also a risk-free asset with gross return Rf = 1.03. Then the
stochastic discount factor is ________ for state A and ________ for state B. (Round results to 4 decimals)
40. Which of the following interpretations is true for Euler equation: \(8) = 8[\(8:=)(1 + B,8:=)] ?
A. The right side is the marginal utility cost of consuming one dollar less at time t.
B. The left side is the expected marginal utility benefit.
C. When left side is lower than the right side, it indicates we should reduce the consumption and increase
the investment.
D. When left side is higher than the right side, it indicates we should reduce the consumption and increase
the investment.
41. When present the return with fundamental equation as 8k61 + B,8:=7l = =<]F^_`&,!(#,a!(#bc![a!(#] , which of the
following interpretations is true?
A. An asset with a high expected return must have high covariance with the stochastic discount factor.
B. When covariance is low with a lower M, the asset tends to have a low return.
C. When an asset performs well in bad time, the left side will be relatively higher than those with poor
performance.
D. When the covariance is low and investors have high marginal utility, the investor will require a higher
expected return.
!
42. According to the equation: rW,X:= = − + ∆8:= − Y$Z%$> , which of the following interpretations is
false?
A. The risk-free rate is high when investors are more impatient.
B. Risk-free rate is linear in expected consumption growth, and its slope coefficient is the coefficient of
relative risk aversion.
C. The risk-free rate is low when time discount factor is high.
D. According to the precautionary savings effect, the investors tend to reduce the saving if they are more
risk averse.
【Week 11】
43. Which of the following statements in terms of two different view on return predictability is true?
A. According to classic view, the stock price will follow random walk and return are predictable in the
efficient market.
B. According to modern view, the competition in stock market will drive out any predictable movement
in stock price.
C. According to classic view, return predictability may be caused by time varying risk premium.
D. According to modern view, if the quantity or price of aggregate risk vary over time, the return may
be predictable in an efficient market.
44. Which of the following statements is false in terms of the estimated regressions of long-horizon returns
on past long-horizon returns by Fama and French?
A. One of the statistical issues is that the sample size is extremely small.
B. Using non-overlapping data may lead to a large sampling error.
C. They find the positive serial correlation in multiple-year return.
D. They find that there is a substantial mean-reversion in stock market prices at longer horizons.
45. Which of the following interpretations is right in terms of forecasting return using dividend price ratio?
A. When stock price is high relative to dividend, it indicates the high return.
B. The regression result shows that the R2 increases as time horizon increases, which indicates the
predictor has higher predictive power.
C. The regression slope coefficients will remain the same as the horizon increases if the predict variable
is persistent.
D. Dividend price ratio correlates with business cycles, there will be a higher risk premium when it is in
bad time.
!
46. Which one of the following statements is false?
A. The diagonal items of covariance matrix under Hansen and Hodrick (1980) method are the same.
B. Use of overlapping observations induce severe serial correlation in the error term.
C. Hansen and Hodrick (1980) standard error only consider and correct the autocorrelation in residuals.
D. The diagonal items from covariance matrix for Hodrick (1992) standard error and Newey-West (1987)
standard error follow the same calculation method.
47. According to Stambaugh Bias, which statement is true? And the bias can be measured by
A. Stambaugh Bias is a bias in predictive variable in finite samples there if the predictor is persistent and
its innovations are correlated with returns.
B. R2 will also be biased but t-test won’t be affected in finite sample.
C. The bias will be downward biased if the two shocks are positively correlated.
D. When is higher, it indicates the predictor is more persistent.
【Week 12】
48. The realized volatility is ________, and the expected volatility is __________.
A. Forward looking; Backward looking
B. Ex-ante volatility; Forward looking
C. Backward looking; Ex-ante volatility
D. Ex-ante volatility; Backward looking
49. Which one of the following statements is true?
A. The term structure of VIX futures prices is always upward-sloping.
B. VIX futures prices are higher than the VIX on average, which indicates short position may outperform
the long position in the long run.
C. We can either buy or sell the VIX to gain profits.
D. We can buy and hold the VIX future to gain profits in the long run.
50. The estimated AR(1) model of the VIX index is 8:= = 0.28 + 0.968 , and we observed the
volatility of Dec 2021 was 25. We can forecast the volatility of Jan 2022 and Feb 2022 is ________ and
________ respectively.
!
Ø Exam Practice Answers
【Week 2】
Q1-Q7 BAECBDD
Q8 $18000; 1000; $22.5
Q9 $7000; $4200; $40
【Week 3】
Q10 20%
Q11 3.75%; 3.68%
Q12-Q13 BC
【Week 4_Markowitz】
Q14 10.20%; 40.11%
Q15-Q17 DCD
【Week 5_SIM】
Q18-Q25 CAABBDAC
【Week 6-8_CAPM & Anomalies】
Q26-Q29 BCBD
Q30 9%
Q31 6.75%; 7.75%; 6.4%; 2.6%
Q32-Q33 BC
【Week 9】
Q34 B
Q35 17.72%; 15.60%
Q36 Portfolio A：0.4907; 8.8333; 1% Portfolio B：0.3373; 10.5000; 2%
Q37 D
【Week 10】
Q38 1) 0.15; 0.1; 0.3; 0.2; 0.2 2) 0.3158 3) 1.7
Q39 0.6380; 1.3037
Q40-Q42 CDD
【Week 11】
Q43-47 DCDCD
【Week 12】
Q48-Q49 CB
Q50 24.28; 23.59
2022S1
Tutor: Mandy
FINC3017
Investment and Portfolio Management
Final Review & Practice Questions
Ø Final Exam Details
Ø 复习建议
ü Lecture & Weekly 相关知识点、概念巩固
ü 至少一遍 Tutorial 题目(解题思路)
ü 独立做题 & 讲解
Final Exam
Exam Date 13:00PM, 16 June 2022 (Sydney Time)
Exam Duration 1 hour and 40 minutes long, including 10 min reading time
Exam Type Open book exam*
Question Type and weight • ~30%: Multiple Choice Questions
• ~70%: Short answer questions (numerical)
Coverage Covers the entire unit but with less emphasis on portfolio theory
*Materials permitted: Matlab, Python, handheld calculator, computer's calculator, a hard copy of a formula sheet and statistical table,
Microsoft Excel, multiple sheets of blank scratch paper and a pen/pencil. Online resources (including Unit of Study Canvas resources,
eBooks and internet search), locally saved notes on the computer and paper-based resources (including printed/handwritten notes and
textbooks). Be mindful that you may not finish the exam within the permitted time if you frequently search for resources to help you
answer the questions.
Open-book exams do not permit the use of third party communication or collaboration apps or websites. Access to any such app or
website is strictly prohibited during your exam and is a serious academic integrity breach.
!
Ø Weekly Contents
Ø Study Guide & Review
² Asset classes and financial instruments
1. Different types of financial instruments
l Equity: Common stock, preferred stock
l Debt: T-bills, T-notes, T-bonds, Corporate bonds, International bonds
l Derivatives: Option (call and put), Future, Forward, Swap
2. How securities are issued and traded
l Primary market V.S. Secondary market
ü Primary market(一级市场): 发行市场，证券首次出售给公众的市场。
ü Secondary market(二级市场): 已发行的有价证券交易、买卖流通的场所。
l IPO/Initial public offering: the first issue of shares to the general public.
l Trading markets:
ü Direct search markets: Buyers and sellers seek each other directly. (the least organized)
ü Brokered markets: Brokers search out buyers and sellers. (不具有买卖资产的所有权)
ü Dealer markets: Dealer purchase assets for their own accounts, and later sell them for a
profit from their inventory.
ü Auction markets: Traders converge at one place to trade.
FINC3017 Weekly Topic
Basic Concepts
Week 1. Introduction • 资产、金融工具的分类、特点
• Buying on margin & short selling理解与
计算Week 2. Asset Classes and Financial Instruments
Portfolio Theory
Week 3. Risk Return Relation and Portfolio Analysis • 相关概念的理解、辨析
• 两类模型的特点、异同对比
（大约2-3题）Week 4. Markowitz Model
Week 5. Single Index Model (Implementing Portfolio Theory)
CAPM & Anomalies
Week 6. CAPM • 相关概念的理解
• 检验的判断、意义
• Anomalies种类和结论Week 7. Testing the CAPM
Week 8. Anomalies
Performance Evaluation Week 9. Performance Evaluation • 定量计算
Asset Pricing Week 10. Asset Pricing Theory • 定性理解
• 定量计算
Current Research
Week 11. Return Predictability • 定性理解
• 可能有简单计算
Week 12. Volatility
!
3. Buying on margin and short selling
相关概念回顾：
ü Initial margin：初始保证金，在建立初始头寸时，投资者需要支付的自有资金.
ü Maintenance margin:需要维持保证金账户自有现金的最低限额.
ü Margin call: 当账户中自有金额低于最低要求时，会触发 margin call 要求补充自有
金额.
l Buying on margin: assume the price will go up and borrow money to purchase the securities.
* Asset (stock value) = Equity (own money) + Liability (borrowed money, 固定)
* Equity in account = stock value – money borrowed + additional funds
* Stock value (market value, 变动)= #number of shares x market price
ü Margin = Equity in AccountStock value = Stock value − borrowed moneyStock value
ü !"#$%& $( )**+#(%,-./#0 +1 2%+*3, = #(#5607 +1 28.702 × 5.730% :7$*0 ; 6+77+<0= 5+(0&#(#5607 +1 28.702 × 5.730% :7$*0 <
l Short selling: assume price will drop and borrow securities to sell, later buy back to cover.
* Asset (Total margin account) = Equity (own money) + Liability (stock owed)
* Initial Equity = Initial margin rate x Initial market value of stock
* (Short Sale) Equity = Total margin account(固定) – Market value of stock
ü = !"#$%&-./#0 +1 2%+*3 = >+%./ 5.7?$( .**+#(% ; -./#0 +1 2%+*3-./#0 +1 2%+*3
ü !"#$%& $( )**+#(%,-./#0 +1 2%+*3, = >+%./ 5.7?$( .**+#(% ; #(#5607 +1 28.702 × 5.730% :7$*0#(#5607 +1 28.702 × 5.730% :7$*0 <
à Receive margin call when: Equity <= Maintenance margin X Market Value of Stock
ASSET LIABILITY
Stock value Equity (own money)
Liability (borrowed money)
ASSET LIABILITY
Total margin account Equity (Deposited own money ± fluctuation)
Liability (market value of short position in securities)
!
² Portfolio theory
1. Risk-return
l Return measurement：
ü Simple net return (HPR) – Single period: 8 = 9!:;!<9!"#9!"# = 9!:;!9!"# − 1
ü Simple gross return – Single period: 1 + 8
ü Asset gross return – Multiple period: 1 + 8() = (1 + 8)(1 + 8<=)(1 + 8<>)… (1 + 8ü Log return – Single period: 8 = (1 + 8) = 0 88<=1 = 8 − 8<=
ü Log return – Multiple period: 8() = log (1 + 8()) = 6(1 + 8)(1 + 8<=)… (1 + 8
l Average Return：
ü Arithmetic average return(算术平均)
ü Geometric average return (几何平均) (1 + @) = (1 + =)(1 + >)… (1 + A)=A
ü Dollar weighted average return (满足下式的 internal rate of return) BCDEFG = FH8DEFG
l Risk measurement：
ü Variance: average/expected value of squared deviations from mean.
ü Standard deviation (): square root of variance, often called volatility.
ü Sharpe Ratio ℎ = ̅B − DB
l Conversion of Annualizing return, Variances, Volatility(年化转换的计算)
!
2. Mean variance analysis
l Risk-return trade-off: 既定风险下的最大收益或既定收益下的最小风险.
l Portfolio return and variance: I = D BBCBJ= I> = D B>B>CBJ= +DDBK(BK)KBLK
l Investment opportunity set
ü 2-Risky Asset: Investment opportunity set is the entire curve (下图左)
ü More than 2: the entire area inside the hyperbola. (下图右)
l Efficient portfolios: portfolios on efficient frontier.
l Efficient frontier: the upper branch of the curve.
l Minimum variance portfolio: the left-most
portfolio.
l Capital market line (CML):
ü Special CAL which is tangent to the efficient
frontier.
ü Highest Sharpe ratio/slope
ü Efficient frontier for portfolios combined
Multiple Risky Assets+ Risk-free Asset
l Tangency portfolio
l Effect of correlation (2-asset): There are benefits to diversification whenever asset returns are
less than perfectly positively correlated -as ρ becomes more negative, more diversification
benefits. (两类资产负相关越强，能达到的分散化优势越强)
l The risk of a large portfolio: The risk of a portfolio with many assets is largely determined by
average covariance risk - correlation/covariance risk can change very quickly.
T-bill
Stock
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00%
Rp
!
3. Markowitz and Single Index Model
l SIM Formula:
ri,t = ai + βimt + ei,t
s : expected return related to firm-specific factor. (个股相关的预期收益率)
s mt: expected return related to market. (市场相关的预期收益率)
s ,t : unexpected return (firm-specific) or residual. (unexpected event 相关的收益率)
l Variance
σi2 = βi2σm2 + σ2(ei)
s βi2σm2: 系统性风险
s σ2(ei): 非系统性风险/公司特有风险
l Covariance Matrix
l Markowitz V.S. SIM
Markowitz Mean-Variance Model Single Index Model
Number of Input Data
(初始需要的数据量)
• N return estimates
• N Variance estimates
• (N2 – N)/2 Covariance estimates
Total = (N2 + 3N)/2
• N α estimates
• N β estimates
• N Variance estimates
• 1 estimate of market return
• 1 estimate of market variance
Total = 3N + 2
Assumptions of return
(假设条件)
• No assumption on return generating process.
• Parameter values obtained by calculating
sample estimates from historical data.
• SIM makes assumptions about the return generating
process.
• The parameters are obtained through the imposed
assumption on data generating process.
Computation issue • More data involved as n increases à difficult to
calculation.
• Easier than Markowitz model.
• Vastly reduced the number of estimates. ! and Covariance Matrix • Estimated from historical data • Calculated based on the estimates obtained from
regression model.
!
² CAPM
1. The link between portfolio theory and the CAPM
l Portfolio theory analyses how investors form their portfolios given asset risk and return
characteristic. (risk-return trade-off)
l CAPM shows how risky assets are priced. It explains:
ü What is tangency portfolio?
ü How does investors’ asset demand determine the relation between assets’ risk and return
in an equilibrium? (重要思想/机制：asset demand = asset supply)
2. Implications of the CAPM (important concepts such as alpha, beta, and SML)
l CAPM Assumption: perfect capital market
l CAPM Formula: [B] = D + B 6[M]−D7 or [B] − D = B ([M] − D) B = (B , M)M>
l Predictions:
ü the tangency portfolio is the market portfolio
ü the expected return on any risky asset E[ri] is given by the above formula
ü the market risk premium can be represented by: [M] − D = ̅M>
l Implications:
1) In equilibrium, the market portfolio is the unique mean-variance efficient tangency portfolio,
and all investors should hold the market portfolio. No one can outperform/beat the market
in the long run, thus a passive strategy is efficient.
2) CAPM equation shows the risk-return relationship (can plot as SMLà return-beta).
3) It implied security risk is related to beta and market risk premium, and only systematic risk
(market risk) will be rewarded. High beta securities are more risky à perform badly when
the market goes down.
4) High beta security should earn high return.
5) It can be used to calculate discount rate/required rate of return/opportunity cost of capital.
6) It provides a benchmark rate of return (SML) for evaluate investment performance, and a
method for performance evaluation of fund/portfolio managers. à using alpha and pursue
positive alpha.
l Alpha/α: the abnormal rate of return on a security in excess of what would be predicted by the
CAPM. (actual expected return – fair expected return via CAPM)
l SML (Security Market Line): Graphs individual asset risk premiums as a function of asset
risk/ asset’s beta.
!
3. Testing the CAPM
l Portfolio sorts: 基于特定特征分类分组排序
l Regression-based approaches
ü Time series regression
回归方程：by running OLS time-series regressions: 8NB = B + B8 + 8B, t = 1,2,3, …, T
s 8NB: the excess return of asset i;
s 8: the excess return of the market;
s Asset can be individual stock or portfolios
检验目标：B = 0；B显著不为 0.
ü Cross-section regression
回归方程: by running a cross-sectional regression of average excess returns on the betas: (8NB) = O + B + B, i = 1,2,3, …, N
检验目标: λ0 = 0; λ = market risk premium > 0.
ü Fama-MacBeth regression
基本回归方程：running a cross-sectional regression at each time period 8NB = O,8 + 8B + B8, t = 1,2,3, … T, for each t
检验目标: SO = 0；S8 = market risk premium
l t-test 判断方法
[当原假设为：检验参数 = 0]
1) t-stat (越大越拒绝)
t-stat > t 临界值 à 落入拒绝域，拒绝原假设，则对应参数显著不为 0.
t-stat < t 临界值 à 不能拒绝原假设，则对应参数显著为 0.
注：t 临界值可以粗略取值为 1.96 或 2.
2) p-value (越小越拒绝)
p-value < significant level (5%) à 拒绝原假设，则对应参数显著不为 0.
p-value > significant level (5%) à 不能拒绝原假设，则对应参数显著为 0.
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -0.0011341 0.006276525 -0.1806863 0.85724367 -0.0136979 0.01142975
Mkt - rf 0.97007904 0.189292106 5.12477282 3.5697E-06 0.59116972 1.34898836
!
4. Anomalies
l Anomalies: the stylized facts that stocks with certain characteristics tend to outperform relative
to others. (可理解为通过实际观测到的数据结果与理论模型得出的结果不同或相违背)
ü Size Effect/ Small-firm Effect: small stocks outperform large stocks.
ü Value Effect (Book-to-market ratio): stocks with high book-to-market ratios (value stock)
outperform those with low book-to-market ratios(growth stock).
ü Profitability anomaly: companies that are more profitable outperform those that are less
profitable.
ü Investment anomaly: companies that do more investments underperform those that do less
investments (e.g. R&D expenditure).
ü Momentum anomaly: Winner stocks outperform loser stocks. (good or bad recent
performance of particular stocks continues over time)
l Interpretations of anomalies
ü Those return patterns/anomalies are due to the mispricing.
ü Nothing wrong with the return pattern, just the pricing model we use is wrong/ cannot
explain the return pattern so well à we may need to consider more realistic model.
² Performance Evaluation
1. Average returns (simple average, time-weighted average, and dollar weighted average)
参考 Portfolio theory
2. Risk adjusted performance measure: Sharpe ratio, M2 , Treynor ratio, and alpha
Formula Implication/意义 Other characteristics
Sharpe ratio
= ̅! − ̅"!
Measurement of excess return per unit
of total risk.
- Dose not rely on particular
asset pricing model.
- May be manipulated.
- Numerical value is difficult
to interpret. # = $∗ − & = (! − &) × &
Comparison of the return between
adjusted portfolio’s return and the
market index, as they have the same
standard deviation.
- Adjust the portfolio(P)
standard deviation to match
with the passive market index
à P*
B = CC = C∗
Treynor
ratio
= ̅! − ̅"!
Measurement of excess return per unit
of systematic risk.
- Needs to estimate beta.
- Appropriateness of CAPM.
Jensen’s
alpha
$ = ̅! − [̅" + !(̅& − ̅")] Measurement of the average return on the portfolio over and above that
predicted by the CAPM.
Alpha is model dependent.
!
² Asset pricing
1. State space model (important concepts such as AD securities and state prices)
l Arrow-Debreu Securities (ADS): it will pay off $1 if state of nature s occurs next period and
zero otherwise. For example：
s=1 s=2 s=3
⎣⎢⎢
⎢⎢⎡
100...0⎦⎥⎥
⎥⎥⎤
⎣⎢⎢
⎢⎢⎡
010...0⎦⎥⎥
⎥⎥⎤
⎣⎢⎢
⎢⎢⎡
001...0⎦⎥⎥
⎥⎥⎤
l State prices/Ws :为当前时点上述 AD Security 的价格，且满足 0< Ws <1.
l Risky asset with random pay off Y can be represented as:
Y =
⎣⎢⎢
⎢⎢⎡
=>Q...R ⎦⎥⎥
⎥⎥⎤
也可通过 AD Securities 表示为：Y = = ⎣⎢⎢
⎢⎢⎡
100...0⎦⎥⎥
⎥⎥⎤ + > ⎣⎢⎢
⎢⎢⎡
010...0⎦⎥⎥
⎥⎥⎤ + Q ⎣⎢⎢
⎢⎢⎡
001...0⎦⎥⎥
⎥⎥⎤+. . . +R ⎣⎢⎢
⎢⎢⎡
000...1⎦⎥⎥
⎥⎥⎤
l State Prices and SDF
à 引入 Physical Probability R = DR RR RR= = DR R RR= = (R R)
l Inferring State Prices from Option Prices (大概率会考计算, 结合/融合上述知识点)
!
2. Link between state prices and risk neutral probabilities
l Risk Neutral Probability 标记为 _R, 且满足 0< _R <1，∑ _RS= = 1， 可表示为： _R = R = R∑ RR=
3. Consumption based asset pricing and the fundamental equation of asset pricing E(MR)=1.
l Fundamental Asset Pricing Equation = [:( + ,:)]
à 可简化为：
E(MR)=1
s R 为 Gross return
s 8:=：(基于 Fundamental Equation)
ü intertemporal marginal rate of substitution of the investor/stochastic
discount factor(SDF)/ pricing kernel/ marginal utility.
ü Random variable and always positive.
ü Economic meaning: High 8:= corresponds to low consumption à
marginal utility is high when the level of consumption is low.
s 等式说明 expected discounted return都是相同的，均为 1；即使不同时间、不
同资产的期望收益可能不同(e.g., 8[1 + B,8:=])
à More general case:
s 8:= /SDF 为正，是基于市场上无套利机会的假设.
s Different asset pricing models use different 8:=. (即不同的折现因子)
s 8:= can be expressed as an index for bad times. (M 越高，则说明越能说明是 bad
times 的情形; 可以理解为当消费者处于 bad time，消费水平比较低/low level of
consumption，边际效用就会越高/high marginal utility)
l 各类变形式及 implications
!
4. Consumption model with power utility (the equity risk premium puzzle, the risk-free rate puzzle,
and HJ bound)
l 各类变形式及 implications
l Equity Risk Premium Puzzle
ü Most economists believe risk aversion γ should be less than 10. (但实际观测到的
值非常高，因此相违背)
ü Power utility model can only fit the equity premium if the coefficient of relative risk
aversion is very large.(需要非常大才能满足相应等式)
l Risk-free rate puzzle
依据等式 : rW,X:= = − + ∆8:= − Y$Z%$>
解读：
若非常大，则等式右侧第二项∆8:=也会较高，如果要使无风险利率满足较低水平，
则需要非常大，需要接近或者大于 1；而作为时间折现因子，合理范围是 0 到 1，但
根据实际的数据，则可能需要大于 1，意味着一个较低的甚至是负向的时间偏好率，
不合理，前后矛盾。
l HJ bound
M ≥ EX kr[,X:=l − rW,X:= + B>2B
ü 依据该公式，SDF 对数形式的标准差应该大于等于市场上资产的最大 Sharpe ratio；
ü 市场资产组合的 Sharpe ratio约为 50%；
ü 结合等式：8:= = − ∆8:= à () = (∆8:=), 需要较大的
[由于市场资产组合的 Sharpe ratio约为 50%，因此意味着M要大于等于 50%，而基于
数据(∆8)相较于()非常小，所以需要较大的满足上述等式.]
*Equity risk premium puzzle 另一视角解读: stochastic discount factor implied from the standard
consumption-based asset pricing models is not volatile enough.
!
² Stock Return Predictability
1. Understanding stock return predictability
l Classic view V.S. Modern View
l Forecasting with
ü Past return
ü Technical indicators
ü Economic variables (D/P ratio)
2. Empirical evidence and interpretation
l D/P ratio & 相关结论
3. Statistical issues of return predictive regressions (e.g., Stambaugh bias)
l Issue 1_ Overlapping data à Traditional OLS standard error not appropriate (理解对应 3种
解决方法)
l Issue 2_Stambaugh bias: a bias in predictive coefficient in finite sample if predictor is
persistent and its shocks are correlated with returns. (其他影响包括 R2和 t-stat 也会有偏差)
² Volatility
1. Different notions of volatility
l Realised/ historical/ backward looking
l Expected/ Ex-ante/ Forward looking
2. Volatility measurement, modeling, and forecasting (理解如何通过模型预测)
3. Understand the economics of volatility derivatives with a focus on VIX futures
!
Ø Exam Practice Questions
【Week 2】
1. Which of the following is a derivative security?
A. Banker’s Acceptance
B. Cross currency swap
C. Preferred stock
D. Commercial Paper
2. Which of the following belongs to money market securities?
A. 6-month T-bill
B. 8-year Corporate Bond
C. 15-year T-Bond
D. 5-year T-Note
3. A purchase of a new issue of stock takes place
A. in the secondary market
B. in the primary market
C. usually with the assistance of an investment banker
D. in the secondary and primary markets
E. in the primary market and usually with the assistance of an investment banker
4. On which of the following market it is most likely to transfer an asset between the third party and
buyer/seller?
A. Direct search market
B. Brokered market
C. Dealer market
D. Auction market
5. Initial margin requirements are determined by
A. the Securities and Exchange Commission
B. the Federal Reserve System
C. the New York Stock Exchange
D. the Federal Reserve System and the New York Stock Exchange
!
6. Jack purchased COL stock at $14 per share. The stock is currently selling at $17. His gains may be
protected by placing a
A. stop-buy order
B. limit-buy order
C. market order
D. limit-sell order
7. Which of the following orders instructs the broker to buy at the current market price?
A. Limit-buy order
B. Limit-sell order
C. Stop-buy order
D. Market order
【Buying on margin】
8. Tom has $12,000 cash on hand and want to buy shares of Company A at $30 from broker using as little
of his own money as possible. The initial margin requirement is 40% and the maintenance margin is 20%.
Tom can borrow _______ as the maximum amount from the broker. Upon borrowing from the broker,
the total number of shares Tom can buy is _______. Tom will receive a margin call if the stock price
drops lower than _________ per share.
【Short selling】
9. Jason decides to short sell 200 shares of stock A with current market price at $35 per share. The total
proceeds he will get from it is ______. The broker set the initial margin as 60%, then he has to deposit
______ to the margin account. If the maintenance margin is 40%, Jason will receive the margin call if
the price increase to more than ______ per share.
【Week 3】
10. An investor purchased one share of stock for $ 40, then received $3 dividend at the end of the month
and sold it for $45. The simple net return is _____.
11. The returns for stock WOW over the past 4 years were 3%, 8%, -2%, 6% respectively, the arithmetic
average return is _______ and geometric average return is ________. (Round to two decimals)
12. The return and variance of Stock BNP in the past three month was 4% and 1.5% respectively, what’s
the annualised return and variance?
A. 12%; 4.5%
B. 16%; 6%
C. 12%; 3%
D. 16%; 3%
!
13. The daily return and variance of Stock COL was 0.05% and 0.1% respectively, what’s the annualised
return and standard deviation?
A. 18.25%; 36.5%
B. 12.6%; 25.2%
C. 12.6%; 50.20%
D. 18.25%; 60.42%
【Week 4_Markowitz】
14. Following the table below, if the correlation is 0.8, the portfolio return is _______ and standard
deviation is ________. (Please present in percentage format and round to 2 decimals)
Stock Return Variance Weight
A 6% 12% 30%
B 12% 20% 70%
15. An investor has a risk aversion coefficient of 5. The expected return and standard deviation of the optimal
risky portfolio are 15% and 25%, respectively. If the Sharpe ratio of the optimal capital allocation line is
0.48, what is the proportion of the investor’s combined portfolio that should be invested in the risky
portfolio that would maximise their utility?
A. 9.6%
B. 19.1%
C. 33.8%
D. 38.4%
16. Treasury bill pays a 6% rate of return. A risk averse investor __________ invest in a risky portfolio that
pays 12% with a probability of 40% or pays 2% with a probability of 60% because __________.
A. might; she is rewarded a risk premium
B. might; the portfolio offers a higher return than the Treasury bill even though it is risky
C. would not; she is not rewarded with any risk premium
D. would not; the risk premium is too small
E. would not; risk averse investors will always choose the risk-free asset
17. The optimal risky portfolio can be identified by finding _____________.
A. the minimum variance point on the efficient frontier
B. the maximum return point on the efficient frontier
C. the tangency point of the security market line and the efficient frontier
D. the efficient portfolio with the highest Sharpe ratio
!
【Week 5_SIM】
18. Which of the following is not the characteristic of SIM?
A. Impose the assumption on data generating process
B. Reduce the number of parameters to estimate
C. Covariance matrix is calculated with historical data
D. Easier than Markowitz on computation
19. A single-index model uses __________ as a proxy for the systematic risk factor.
A. a market index, such as the S&P 500
B. the current account deficit
C. the growth rate in GNP
D. the unemployment rate.
20. As diversification increases, the firm-specific risk of a portfolio approaches
A. 0.
B. 1.
C. infinity.
D. (n – 1) × n.
21. The index model has been estimated for stocks A and B with the following results:
RA = 0.02 + 0.5RM + eA
RB = 0.01 + 0.8RM + eB
σM = 0.25; σ(eA) = 0.20; σ(eB) = 0.15
The covariance between the returns on stocks A and B is
A. 0.0625
B. 0.0250
C. 0. 2200
D. 0.0380
22. Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope
of the regression line is an estimate of
A. the α of the asset
B. the β of the asset
C. the σ of the asset
D. the δ of the asset
!
23. In single index model, the return on a stock in a particular period will be related to
A. firm-specific events
B. macroeconomic events
C. the error term
D. both firm-specific events and macroeconomic events
24. Assume that stock market returns do not resemble a single-index structure. An investment fund
analyses 120 stocks in order to construct a mean-variance efficient portfolio constrained by 150
investments. They will need to calculate _____________ expected returns and ___________ variances
of returns.
A. 120; 120
B. 120; 14400
C. 14400; 120
D. 14400; 14400
25. An investment fund analyses 125 stocks in order to construct a mean-variance efficient portfolio and
single index model respectively constrained by 125 investments. They will need to calculate
_________ covariances for mean-variance model and _________ variance for single index model.
A. 125; 125
B. 15625; 125
C. 7750; 125
D. 15625; 15625
【Week 6-8_CAPM & Anomalies】
26. Which of the following is on the horizontal axis in a plot of the Security Market Line?
A. Standard deviation
B. Beta
C. Expected return
D. Risk premium
27. According to the CAPM, the market portfolio has a beta of _____ and the intercept of the security
market line is _______. (Y-axis represents the excess return)
A. 0, 0
B. 0, risk-free rate
C. 1, 0
D. 1, risk-free rate
!
28. In the context of the CAPM, the relevant risk is
A. unique risk.
B. systematic risk.
C. standard deviation of returns.
D. variance of returns.
29. According to the CAPM, which of the following is true?
A. The expected return of an asset with beta of zero is zero.
B. The slope of the security market line is the Sharpe ratio of the market portfolio.
C. The X-axis of SML is the standard deviation of the investment asset/portfolio.
D. All else equal, the higher the alpha, the better the investment is.
30. The expected return on market is 7% and the risk-free rate is 3%. The beta of CBA is 1.5. According to
the CAPM, the expected rate of return of CBA is ________.
31. Assume the risk-free rate is 1% and the average investor has a risk-aversion coefficient of A = 3. We
also know the standard deviation of the market portfolio and stock JBH is 15% and 20% respectively.
The JBH has a beta of 0.8. According to the CAPM, the equilibrium value of the market risk premium
is _________, the expected return on the market is _________, and the expected rate of return on JBH
is __________. If the historical return of JBH is 9%, the alpha of JBH is ________.
32. A fund manager has managed a portfolio, which had an average annualized return of 12% with standard
deviation of 8% over the last 5 years, and its estimated beta during the period was 0.6. Suppose over the
sample period, the risk-free rate is 4% and the average return on the market is 11%. What was the
manager’s alpha? Did the manager exhibit positive performance ability according to the CAPM?
A. 2.8%; Yes
B. 3.8%; Yes
C. -3.8%; No
D. -2.8%; No
33. The analyst tries to estimate the following cross-sectional regression of average excess returns of the
various sectors under managed portfolios on their betas and volatilities: ri = λ0 + λ1betai + λ2voli + ei,
according to the CAPM, what should we expect for λ0, λ1, and λ2?
A. 0, 0, 0
B. market return, 0, 0
C. 0, market risk premium, 0
D. 0, 0, market risk premium
!
34. According to the size effect, what would be the best way to construct the trading strategy?
A. long small stock and large stock at the same time
B. long small stock and short large stock
C. short small stock and long large stock
D. short small stock and short large stock at the same time
【Week 9】
35. Jason purchased a share of stock for $20 at the beginning of year 1. At the end of year 1, he received $2
dividend and purchased one more share for $23. At the end of year 2, he received $1 dividend and sold
two shares for $25 each. The geometric average return is _______ and dollar weighted return is ______.
36. Consider the two excess return index models for portfolio A and B, the risk-free rate over the period was
6% and the market’s average return was 14%. (Round results to 4 decimal place)
PORTFOLIO A PORTFOLIO B
Model Estimates 1% + 1.2(rm-rf) 2% + 0.8(rm-rf)
R squared 55% 48%
Residual Standard Deviation 10.3% 19.5%
Standard Deviation of Portfolio 21.6% 24.9%
For Portfolio A, the Sharpe Ratio is ________, the Treynor ratio is ________ and alpha is_________.
For Portfolio B, the Sharpe Ratio is ________, the Treynor ratio is ________ and alpha is_________.
37. A portfolio generates an annual return of 14%, a beta of 1.5, and a standard deviation of 16%. The
market index return is 10% and has a standard deviation of 12%. What is the M2 measure of the portfolio
if the risk-free rate is 2%? What’s the weight in risk-free asset?
A. 4%; 75%
B. 1%; 75%
C. 4%; 25%
D. 1%; 25%
!
【Week 10】
38. Suppose the state of nature is summarized by the value of the market portfolio which has a discrete
probability distribution with possible values of: [$1, $2, $3, $4, $5]. Call options on the market portfolio
with different strike prices are available and their prices are given below:
1) Using the above information, calculate the price of the Arrow-Debreu security for each state.
2) What is the risk neutral probability of the state where the value of the market portfolio is equal to $3?
3) What is the price of a put option with a strike price of $5?
39. Consider a single period economy which can enter into one of two possible states (A, B). Each of these
states occurs with equal probability. In state A, a risky asset will have a net return of 0.5, while in state
B it will have a net return of -0.2. There is also a risk-free asset with gross return Rf = 1.03. Then the
stochastic discount factor is ________ for state A and ________ for state B. (Round results to 4 decimals)
40. Which of the following interpretations is true for Euler equation: \(8) = 8[\(8:=)(1 + B,8:=)] ?
A. The right side is the marginal utility cost of consuming one dollar less at time t.
B. The left side is the expected marginal utility benefit.
C. When left side is lower than the right side, it indicates we should reduce the consumption and increase
the investment.
D. When left side is higher than the right side, it indicates we should reduce the consumption and increase
the investment.
41. When present the return with fundamental equation as 8k61 + B,8:=7l = =<]F^_`&,!(#,a!(#bc![a!(#] , which of the
following interpretations is true?
A. An asset with a high expected return must have high covariance with the stochastic discount factor.
B. When covariance is low with a lower M, the asset tends to have a low return.
C. When an asset performs well in bad time, the left side will be relatively higher than those with poor
performance.
D. When the covariance is low and investors have high marginal utility, the investor will require a higher
expected return.
!
42. According to the equation: rW,X:= = − + ∆8:= − Y$Z%$> , which of the following interpretations is
false?
A. The risk-free rate is high when investors are more impatient.
B. Risk-free rate is linear in expected consumption growth, and its slope coefficient is the coefficient of
relative risk aversion.
C. The risk-free rate is low when time discount factor is high.
D. According to the precautionary savings effect, the investors tend to reduce the saving if they are more
risk averse.
【Week 11】
43. Which of the following statements in terms of two different view on return predictability is true?
A. According to classic view, the stock price will follow random walk and return are predictable in the
efficient market.
B. According to modern view, the competition in stock market will drive out any predictable movement
in stock price.
C. According to classic view, return predictability may be caused by time varying risk premium.
D. According to modern view, if the quantity or price of aggregate risk vary over time, the return may
be predictable in an efficient market.
44. Which of the following statements is false in terms of the estimated regressions of long-horizon returns
on past long-horizon returns by Fama and French?
A. One of the statistical issues is that the sample size is extremely small.
B. Using non-overlapping data may lead to a large sampling error.
C. They find the positive serial correlation in multiple-year return.
D. They find that there is a substantial mean-reversion in stock market prices at longer horizons.
45. Which of the following interpretations is right in terms of forecasting return using dividend price ratio?
A. When stock price is high relative to dividend, it indicates the high return.
B. The regression result shows that the R2 increases as time horizon increases, which indicates the
predictor has higher predictive power.
C. The regression slope coefficients will remain the same as the horizon increases if the predict variable
is persistent.
D. Dividend price ratio correlates with business cycles, there will be a higher risk premium when it is in
bad time.
!
46. Which one of the following statements is false?
A. The diagonal items of covariance matrix under Hansen and Hodrick (1980) method are the same.
B. Use of overlapping observations induce severe serial correlation in the error term.
C. Hansen and Hodrick (1980) standard error only consider and correct the autocorrelation in residuals.
D. The diagonal items from covariance matrix for Hodrick (1992) standard error and Newey-West (1987)
standard error follow the same calculation method.
47. According to Stambaugh Bias, which statement is true? And the bias can be measured by
A. Stambaugh Bias is a bias in predictive variable in finite samples there if the predictor is persistent and
its innovations are correlated with returns.
B. R2 will also be biased but t-test won’t be affected in finite sample.
C. The bias will be downward biased if the two shocks are positively correlated.
D. When is higher, it indicates the predictor is more persistent.
【Week 12】
48. The realized volatility is ________, and the expected volatility is __________.
A. Forward looking; Backward looking
B. Ex-ante volatility; Forward looking
C. Backward looking; Ex-ante volatility
D. Ex-ante volatility; Backward looking
49. Which one of the following statements is true?
A. The term structure of VIX futures prices is always upward-sloping.
B. VIX futures prices are higher than the VIX on average, which indicates short position may outperform
the long position in the long run.
C. We can either buy or sell the VIX to gain profits.
D. We can buy and hold the VIX future to gain profits in the long run.
50. The estimated AR(1) model of the VIX index is 8:= = 0.28 + 0.968 , and we observed the
volatility of Dec 2021 was 25. We can forecast the volatility of Jan 2022 and Feb 2022 is ________ and
________ respectively.
!
Ø Exam Practice Answers
【Week 2】
Q1-Q7 BAECBDD
Q8 $18000; 1000; $22.5
Q9 $7000; $4200; $40
【Week 3】
Q10 20%
Q11 3.75%; 3.68%
Q12-Q13 BC
【Week 4_Markowitz】
Q14 10.20%; 40.11%
Q15-Q17 DCD
【Week 5_SIM】
Q18-Q25 CAABBDAC
【Week 6-8_CAPM & Anomalies】
Q26-Q29 BCBD
Q30 9%
Q31 6.75%; 7.75%; 6.4%; 2.6%
Q32-Q33 BC
【Week 9】
Q34 B
Q35 17.72%; 15.60%
Q36 Portfolio A：0.4907; 8.8333; 1% Portfolio B：0.3373; 10.5000; 2%
Q37 D
【Week 10】
Q38 1) 0.15; 0.1; 0.3; 0.2; 0.2 2) 0.3158 3) 1.7
Q39 0.6380; 1.3037
Q40-Q42 CDD
【Week 11】
Q43-47 DCDCD
【Week 12】
Q48-Q49 CB
Q50 24.28; 23.59
