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ECON5007
The Economics of Financial Markets:
Portfolio Theory and the Capital Asset
Pricing Model
Grace Ye
The University of Sydney
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Overview
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Holding Period Return
HPR is the total return earned by an investor over a single period and it
includes all cash flows occurring at the end of the period.
Calculation:
P1−P0+CF1
P0
or,
FV − PV
PV
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Time-weighted Rate of Return
Time-weighted rate of return measures the compound rate of growth.
• Calculation
Firstly, calculate the HPR on the portfolio for each subperiod;
Then, compute the annualized TWRR.
TWRR =

ς=1
1 + − 1,
where = number of years;
= number of periods.
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Example - TWRR
Assume Sinan purchases a share of stock for $50 at time t = 0, and another
share at $65 at time t = 1, and at the end of Year 1 and Year 2, the stock
paid a $2 dividend. Also, at the end of Year 2, Sinan sold both shares for
$70 each. The time-weighted rate of return on the investment is:
A. 18.27%.
B. 20.13%.
C. 21.83%.
Correct Answer: C
HPR1 = (65+2)/50−1=34%,
HPR2 = (140+4)/130−1=10.77%
Time-weighted return = [(1+34%) × (1+10.77%)]^0.5− 1 = 21.83%
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Money-weighted Rate of Return
Money-weighted Rate of Return is the IRR based on the cash flows related to
the investment.
• Calculation
Firstly, determine the timing of each cash flow;
Then, using the calculator to compute IRR.
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Example - MWRR
Assume Sinan purchases a share of stock for $50 at time t = 0, and another
share at $65 at time t = 1, and at the end of Year 1 and Year 2, the stock
paid a $2 dividend. Also, at the end of Year 2, Sinan sold both shares for
$70 each. The money-weighted rate of return on the investment is:
A. 15.45%.
B. 16.73%.
C. 18.02%.
Correct Answer: C
CF0=-50, CF1=-65+2=-63, CF2=(70+2)×2=144
Calculate IRR=18.02%
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TWRR vs MWRR
The relationship between TWRR and MWRR
• Both TWRR and MWRR are annual rates.
• Time-weighted return is not influenced by cash flow, but money- weighted
return will be affected by cash flow.
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The portfolio on the minimum-variance frontier with the lowest
standard deviation is:
A. Unattainable.
B. The optimal risky portfolio.
C. The global minimum-variance portfolio.
Correct Answer: C.
Example - Minimum-Variance Frontier
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Example - Efficient Frontier
Which of the following statements is least accurate? The efficient
frontier is the set of all attainable risky assets with the:
A. Highest expected return for a given level of risk.
B. Lowest amount of risk for a given level of return.
C. Highest expected return relative to the risk-free rate.
Correct Answer: C.
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Types of Investors
Risk seeking:
• Prefer higher risk to lower risk for a given level of expected returns.
Risk neutral:
• An investor is indifferent about the gamble or the guaranteed outcome.
Risk averse:
• Prefer lower to higher risk for a given level of expected returns.
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Utility Theory
Indifference Curve for various types of investors
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Example
With respect to the mean-variance theory, the optimal portfolio for an
investor is determined by each individual investor’s:
A. Risk-free rate.
B. Borrowing rate.
C. Risk preference.
Correct Answer: C.
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Example - Capital Market Line
Sinan holds 50% risk-free assets ( = 0.04) and 50% portfolio M ( =
0.12; = 0.16). What would the portfolio returns and standard deviations
look like?
• = + = 0.5 × 0.04 + 0.5 × 0.12 = 0.08
•
2 =
2
2 +
2
2 + 2
• Note: Risk-free assets have 0 variance.
•
2 =
2
2 = 0.520.162
• = 0.5 × 0.16 = 0.08
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SML vs CML
SML CML
Measure of
risk
Use systematic risk (non-
diversifiable risk)
Use standard deviation
Application Tool used to determine
the appropriate
expected returns for
securities
Tool used to determine the
appropriate asset allocation for
investors
Definition Graph of the capital
asset pricing model
Graph all the combination of
the risk-free asset and the
market portfolio
Slope Market risk premium Sharpe ratio
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• The risk-free rate is 3% p.a., and the expected return on the market
portfolio is 11%. Shares in company A have a beta of 1.2 and are
currently priced to provide a return of 13%. Which of the following
statements is correct?
• A is underpriced and lies above the security market line
Expected A
return

market risk beta
Application of CAPM
How to judge if a stock is properly valued
= + −
=0.03+1.2（0.11-0.03）
=0.126
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Application of CAPM
How to judge if a stock is properly valued
• Undervalued (X, Y, Z)
i. Estimated return > Required return from the SML
ii. Investors should buy.
• Overestimated (O)
i. Estimated return < Required
return from the SML
ii. Investors should sell.
• Properly valued (M)
i. Estimated return = Required return from the SML
ii. Investors are indifferent between buying or selling.