FINS5513 Lecture 4
SIM and Active Investing
FINS5513 Lecture 4
SIM and Active Investing
FINS5513 Lecture 4
SIM and Active Investing
2❑ 4.1 SIM Regression: The Security Characteristic Line
➢ Applying the SIM
❑ 4.2 Portfolio Construction Under SIM vs Markowitz
➢ SIM and Diversification
➢ CAPM/SIM vs Markowitz Optimisation
❑ 4.3 What Is Active Investing?
➢ Identifying Mispriced Assets
➢ Active Investing Return Objectives
❑ 4.4 Active Portfolio Construction
➢ The Treynor-Black Model
➢ Performance Measures for Active Investing
Lecture Outline
4.1 SIM Regression:
The Security
Characteristic Line
FINS5513
4Applying the SIM
FINS5513
5❑ Say we wanted to determine the relationship between the returns on a single stock and the
market by way of regression. As a minimum we would want to know:
➢ How the stock moved with the market – its
➢ The portion of the stock’s return which is NOT explained by market movements – its
➢ The volatility of the stock’s return including the proportional volatility coming from market
movements vs firm-specific factors – it’s total risk, systematic risk and unsystematic risk
➢ The proportion of the stock’s movement which is explained by market movements – it’s R2
➢ We may even want to plot the relationship graphically
❑ In the simplest case - regressing a single stock against the market – we have only two
variables:
➢ The dependent variable – stock returns (or excess returns) which we plot on the y-axis
➢ The independent variable – market returns (or excess returns) which we plot on the x-axis
➢ This graphical representation is called the Security Characteristic Line (SCL)
SIM Regression
6❑ As an example, assume we are regressing HP’s (Hewlett Packard) excess returns against the
S&P500’s excess returns (as a proxy for the market). We use the following equation:
= + RS&P500 +
❑ If we had 5 years of monthly data, we would have 60 monthly observations. Each plot point
on our graph represents a monthly observation (from BKM 8.3)
Security Characteristic Line Example 1 - HP
Slope is
the
Intercept
is the
Line of best fit
or “fitted line”
Residuals

Security
Characteristic
Line (SCL)
❑ The line of best fit (or fitted line) is the
regression line which best describes the
relationship between and RS&P500
➢ The is the intercept
➢ The β is the slope
➢ The residuals represent deviations
from the fitted line
7❑ The correlation between HP and the market is 0.72 and the market explains about 52% of the
variation in HP (the R2)
❑ HP’s is 0.86% per month (10.32% annually) but it is not statistically significant
❑ HP’s is 2.035 with a 95% confidence interval (+/- 1.96 × standard error) ≈1.54 - 2.53
❑ HP’s is insignificant and the 95% confidence interval for it’s is between 1.54 - 2.53
HP’s SCL Regression Statistics Example 1
Correlation
Coefficient
R2 is the % of HP’s
movement explained
by the market


Significance
testing of and
8❑ Using monthly data from “Berkshire Hathaway SCL” (486 observations) plot the SCL by
regressing monthly BRK excess returns against the monthly market excess returns. Interpret
your results - is and significant, what does the R2 indicate?
Security Characteristic Line Example 2 - BRK
-10.00%
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
-15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00%
Ex
ce
ss
S
to
ck
Re
tu
rn
Excess Market Return
BRK.A Security Characteristic Line Monthly
Predicted Stock Excess Returns (Ri)
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
-15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00%
Ex
ce
ss
S
to
ck
Re
tu
rn
Excess Market Return
BRK.A SCL (Blue) with Residuals (Red) Monthly
Predicted Stock Excess
Returns (Ri)
Slope is
the
Intercept
is the
Line of best
fit or “fitted
line”
Residuals

Security
Characteristic
Line (SCL)
Video: “How to Plot the SCL Using Excel” Excel: “Berkshire Hathaway SCL”
9❑ The correlation between HP and the market is 0.44 and the market explains about 20% of the
variation in BRK (the R2)
❑ BRK’s is 1.11% per month (13.4% annually) and it is statistically significant at the 99%
confidence interval
❑ BRK’s is 0.698 with a 95% confidence interval (+/- 1.96x standard error) ≈ 0.57 – 0.82
❑ BRK’s is significant and high and it’s is low (95% confidence interval of 0.57 – 0.82)
Regression Statistics
Multiple R 0.444341315
R Square 0.197439205
Adjusted R Square 0.195781021
Standard Error 0.062203481
Observations 486
ANOVA
df SS MS F Significance F
Regression 1 0.460712701 0.460712701 119.0695777 6.18982E-25
Residual 484 1.872728127 0.003869273
Total 485 2.333440828
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.011130915 0.002849682 3.90602051 0.00010717 0.00553164 0.01673019
X Variable 1 0.698217453 0.063986786 10.91190074 6.18982E-25 0.572491261 0.823943644
Regression Statistics
Multiple R 0.444341315
R Square 0.197439205
Adjusted R Square 0.19578102
Stan ard Error 0.062203 1
Observations 6
ANOVA
df SS MS F Significance F
Regression 1 .4 0712701 0.460712701 119.0695777 6.18982E- 5
Residual 484 1.872728127 0.003869273
Total 485 2.333440828
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.011130915 0.002849682 3.90602051 0.00010717 0.00553164 0.01673019
X Variable 1 0.698217453 0.063986786 10.91190074 6.18982E-25 0.572491261 0.823943644
BRK’s SCL Regression Statistics Example 2
Correlation
Coefficient
R2 is the % of BRK’s
movement explained
by the market


Significance
testing of and
Mini Case Study: “Can Buffett’s Alpha Be Explained?”
4.2 Portfolio
Construction Under
SIM vs Markowitz
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SIM and Diversification
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❑ The SCL fitted line represents the systematic return component (due to market movements)
➢ The residuals represent deviations from the predicted or expected return (the fitted line)
• We categorise all of these deviations as firm-specific movements (unsystematic)
➢ If the observations hug the fitted line, much of the asset’s movement is caused by market
movements (high R2) and its risk is mostly systematic. If the observations are dispersed,
much of the asset’s movement is firm-specific (a low R2) and its risk is mostly unsystematic
➢ By grouping a number of stocks into a diversified portfolio, firm-specific movements offset
each other, reducing unsystematic risk - the observations will hug the fitted line
Single Stock Well Diversified Portfolio
Unsystematic Risk Under SIM


SCL
13
❑ Let’s see why unsystematic risk can almost be eliminated by a well-diversified portfolio
❑ The residual (unsystematic) variance of an equally-weighted portfolio of n assets is given by:

2 =
σ=1
2
2
❑ In other words, we add all the residual variances of each individual asset in our portfolio and
rather than dividing by n, we divide by n2 to obtain portfolio residual variance
➢ When n gets large, 1
2
→ 0 and
2 becomes negligible
➢ Firm-specific / unsystematic risk (residual variance) is diversified away
❑ The more assets in the portfolio:
➢ The more unsystematic risk is eliminated
➢ However, portfolio systematic risk will not be eliminated - it will converge to market risk 2 ,
because portfolio converges to 1 (from the equation in 3.3: 2 = 2 2 +
2 )
Unsystematic Risk Under SIM
14
Unsystematic Risk Falls With Diversification
❑ A portfolio of around 25-30 uncorrelated stocks almost fully eliminates unsystematic risk
❑ From BKM Figure 8.2
Unsystematic Risk
Number of portfolio stocks n


15
CAPM/SIM vs Markowitz
Optimisation
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❑ One of the reasons the CAPM is widely used is because it is simple and intuitive
➢ Asset ’s risk premium is linearly related to the market risk premium according to it’s
❑ The Markowitz model has many inputs: [1 + + + (2 − )/2]
➢ 1 risk-free rate
➢ sample expected returns
➢ Matrix: sample variances and (2 − ) / 2 sample covariances
➢ When = 50 ➔ 1,326 inputs; = 100 ➔ 5,151; = 5000 ➔ 12,506,501
➢ Using the Markowitz model can therefore lead to calculation errors such as:
• Measurement errors, sampling errors, internally inconsistent correlations etc
❑ A key advantage of the CAPM relative to the Markowitz model is that it dramatically reduces
the inputs required, by relating returns to one common factor – the market return:
➢ Rather than running covariances between each individual asset in the portfolio with every
other asset in the portfolio, each asset’s risk is measured simply by its
CAPM/SIM vs Markowitz Optimisation
17
❑ SIM model: total parameters for stocks
= means + variances + ’s + 3 (i.e.: , () , 2 ) = 3( + 1)
❑ Full Markowitz model may be better in principle, but
➢ High number of inputs increases the chance of estimation error
❑ SIM reduces the number of inputs
➢ Total = 303 when =100 as compared to 5,151
❑ Easier to understand the source of the diversification benefit
➢ SIM segregates systematic and unsystematic portfolio risk
❑ Easier for security analysts to specialise:
➢ Specialise in industry analysis (e.g., determine across industries)
➢ Specialise in firm-specific analysis (e.g., determine based on detailed security analysis)
Single Index Model Advantages
18
❑ BKM (8.5) provides an example comparing the SIM and full covariance (Markowitz) models
➢ As the figure below shows, they produce very similar estimates of the efficient frontier
BKM: SIM vs Markowitz Efficient Frontier
19
❑ The resulting portfolio weights for the GMVP and the optimal risky portfolio ∗ are similar
(even with just a 6-stock portfolio)
❑ A key learning outcome of iLab is to compare the two approaches and produce a similar table
to this (BKM 8.5 and spreadsheet 8.1)
BKM: SIM vs Markowitz GMVP and ∗
4.3 What Is Active
Investing?
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Identifying Mispriced Assets
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❑ Recall:
➢ Assets correctly priced by the CAPM plot on the SML in equilibrium
➢ In the graph below, assets A and C are mispriced i.e., ≠ 0
➢ In a CAPM equilibrium, this should not occur - this is therefore not a CAPM equilibrium
Mispriced Assets
rf
M

( )irE SML
A
B
C
αA < 0
αC > 0
For Asset A
< 0 ∴ it is
overpriced
For Asset C
> 0 ∴ it is
underpriced
23
❑ When the market is not in a CAPM equilibrium
➢ We can seek to find assets that exhibit (mispriced assets according to the CAPM)
➢ If includes mispriced assets, it is no longer the portfolio with the highest Sharpe ratio
➢ Therefore, passive investing (holding ) is not the optimal investing strategy
➢ An active investing strategy with non-market weight in assets exhibiting persistent (ex-ante)
should achieve a higher Sharpe ratio than and “beat the market”
❑ Identifying assets which will exhibit persistent in the future requires a high degree of
investing skill. Persistent can be present because either:
I. Our model which identified (ex-ante) is correct, and the asset is mispriced
II. Our model does not capture all variables impacting price and we need to add more
factors/independent variables to explain the ex-ante (multi-factor models)
❑ We will look at possibility I in 4.4 and possibility II week 5
Seeking
24
Active Investing Return
Objectives
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❑ The objective of active investing is to earn a return higher than some defined benchmark
➢ To achieve this, active investors buy under-priced assets and sell/short over-priced assets
➢ The benchmark may be defined in absolute or relative terms
❑ Absolute returns
➢ The return a fund aims to achieve over a defined period (no index or benchmark is used)
➢ Often stated as a fixed nominal return (e.g., 12.0% p.a.) or a real return (above inflation)
➢ Aims to deliver a positive return over time, irrespective of the wider market performance
➢ Frequently employed by hedge funds to provide “market-neutral” returns
❑ Relative returns:
➢ Return measured relative to a benchmark
➢ The benchmark is a measure of the market that the fund invests in
➢ Example: large-cap U.S equity funds would aim for a return at least equal to the S&P500
➢ Some funds also target returns above an interest rate benchmark e.g., LIBOR + 4%
Return Objectives
26
❑ The benchmark chosen by a portfolio manager should be representative of the universe of
assets from which the manager makes asset selections
❑ Security market indices (e.g., the ASX 200) are often used as the benchmark
❑ Value weighted indices
➢ By far the most common type of indices
➢ Market capitalisation weighted
➢ Have the advantage of requiring minimal amendment over time
➢ Float adjusted market capitalisation weighted indices only account for securities in the index
which are available for purchase by the investing public
• The S&P500 is float adjusted
❑ Note that active managers as a group will not outperform the benchmark – some will
outperform and some will underperform
➢ Active management is zero sum game
Choosing A Benchmark
27
Active Manager Value Add
❑ The “active return” or value-add of an actively managed portfolio is often simply calculated as
the difference between the benchmark performance and the fund’s performance:
= −
= Active return
= Portfolio return
= Benchmark return
❑ A risk-adjusted value-add, which can be described as the portfolio’s , incorporates the
portfolio’s risk relative to the benchmark, often captured by its and stated as:
= −
= Portfolio alpha = Portfolio beta
❑ The more common use of the term “alpha” when referring to fund manager performance is the
non-risk adjusted active return defined simply above
❑ We will look more closely at fund manager performance attribution in week 8
4.4 Active Portfolio
Construction
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The Treynor-Black Model
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❑ Recall that has the highest Sharpe ratio when all assets are correctly priced (equilibrium)
➢ However, this is no longer the case when there are mispriced assets (disequilibrium) –i.e.,
when there are assets that exhibit alpha
➢ The opportunity therefore exists to construct a portfolio with a higher Sharpe ratio than
❑ By constructing an active portfolio of mispriced assets (), an active manager can combine an
active position in with a passive position in the market portfolio (), to form a new optimal
risky portfolio ∗ (comprising and ) with a higher Sharpe ratio than alone
➢ Denote the optimal weighting in the active portfolio as ∗
➢ Denote the optimal weighting in the passive portfolio as (1 − ∗)
Introduction
31
Market Portfolio
1 7 … …
2 8 … …
3 9 … …
4 10 … …
5 11 … …
6 12 …
Active Portfolio
1
2
3
4
5
6
❑ If an active manager has identified multiple mispriced assets exhibiting alpha, the first
decision that needs to be made is, how to construct an optimally weighted Active Portfolio ?
∗
∗ ( − ∗ )
Find ∗ such that the Sharpe ratio of ∗ is greater than the Sharpe ratio of : ∗ >
Combining and
32
❑ We weight our Active Portfolio according to a reward/risk analysis:
➢ The reward of active investing is the additional alpha generated in the Active Portfolio
➢ The risk/cost is the additional unsystematic risk introduced
2 or “tracking error”
❑ We can think of this as if we were “buying” the benefit of mispricing at the cost of taking on
unsystematic risk (tracking error)
➢ We weigh these effects against each other (reward-to-risk)
➢ The ratio at which we can “buy mispricing” is


2
➢ This is the same principle of “buying” excess return by taking on risk when constructing ∗
(optimising the reward-to-risk ratio)
❑ This ratio determines how much we tilt our portfolio towards the Active Portfolio – the higher
the reward-to-risk ratio

2 the more we allocate to
Constructing the Active Portfolio
33
❑ When > 0, we buy the mispriced asset (or assets) - positive active weight
❑ When < 0, we sell the mispriced asset (or assets) - negative active weight
❑ The higher is ∗, the more extra return per unit of (unsystematic) risk we get from our Active
Portfolio (relative to the return per unit of risk from ) – so we increase the weight in
❑ The mispriced Active Portfolio allows us to construct a “new efficient frontier” of risky assets,
with a new ∗ and associated ∗
Constructing the Active Portfolio
rf
M

( )irE CALMA
P*
CALP*
34
❑ Step #1: Calculate the reward to risk-ratio of each asset in the Active Portfolio
➢ Take the alpha of each asset in the Active Portfolio and divide by that asset’s
unsystematic risk
2 :


2
❑ Step #2: Weight each asset in the Active Portfolio based on its reward-to-risk ratio as a
percentage of the sum of all reward-to-risk ratios in the Active Portfolio :
➢ So the weight of the th mispriced asset in the Active Portfolio would be:
=
Τ
2
σ=1
ൗ
2
❑ Step #3: Based on the weightings derived in Step#2, calculate the Active Portfolio’s alpha,
beta and unsystematic risk: , and
2
➢ Next slide shows portfolio calculations
Active Portfolio Weightings
35
❑ We know portfolio expected return is a weighted average of individual asset expected returns:
= ෍
=1

()
❑ Similarly, portfolio is the weighted average of the of individual assets in the portfolio:
= ෍
=1


❑ And portfolio is also a weighted average of the of individual assets in the portfolio:
= ෍
=1


❑ Lastly portfolio unsystematic risk
2 is given by:

2 = ෍
=1


2
2
Active Portfolio ,

36
❑ Step #4: Weight the Active Portfolio relative to the Market according to ’s reward-to-risk
ratio relative to ’s reward-to-risk ratio
➢ The denominator is the market’s reward-risk-ratio (using variance as the definition of risk to
keep the calculations consistent)

0 =
Τ
2
Τ()
2
❑ Step #5: Finally, adjust for the beta of the Active Portfolio as the passive market portfolio
provides less diversification benefit when its beta is higher:

∗ =

0
1 +
0(1 − )
Note: when = 1,∗ = 0
when > 1,∗ > 0
when < 1,∗ < 0
Active Portfolio Allocation ∗
37
❑ Active Fund has identified a single asset that it forecasts will exhibit future alpha. The risk-
free rate is = 2.0%. The market and ’s risks and returns are as follows:
Determine if is mispriced, and if so, construct an optimally weighted ∗ combining and .
➢ Step #1: Calculate alpha (“reward”): = () − − [() − ]
= 0.13 − 0.02 − 1.2 × 0.1 − 0.02 = 0.014 = 1.4%
➢ Calculate unsystematic risk (“cost”): 2 = 2 2 +
2 ↔
2 =
2 −
2
2

2 = 0.42 − 1.22 × 0.252 = 0.07
➢ Calculate reward-to-risk ratio:


2 =
0.014
0.07
= 0.2
Example: Single Mispriced Asset
Risk/Return Market Mispriced Asset
Expected Return () = 10% () = 13%
Risk (standard deviation) = 25% = 40%
Beta = 1.0 = 1.2
38
Example: Single Mispriced Asset
➢ Step #2: This step can be ignored because with a single asset we don’t need to
appropriately weight the Active Portfolio – the Active Portfolio is just 100% in a single asset
➢ Step #3: This step can be ignored because with a single asset we already know the alpha,
beta and unsystematic risk
➢ Step #4: Derive the optimal weight in the mispriced asset by relating its reward-to-risk to the
market’s reward-to-risk:

0 =
Τ
2
Τ()
2 = ൗ0.2
0.1 −0.02
0.252
= 0.15625
➢ Step #5: Adjust for beta:
∗ =

0
1+
0(1−)
=
0.15625
1+0.15625×(1−1.2)
= 0.16129
➢ Therefore our optimal risky portfolio ∗ would be to put ∗ = 16.13% in the mispriced asset
and 83.87% in the market
39
❑ Alpha Fund has identified three stocks which it forecasts will exhibit alpha in the future. It
wishes to construct an appropriately weighted Active Portfolio and determine how much to
allocate to vs a passive investment in the market portfolio . The risk-free rate is =
2.0%. The market and stock risks and returns are as follows:
Construct an optimally weighted Active Portfolio , and then construct an optimally weighted
∗ combining and .
➢ Step #1: and 2 are provided, so we only need to convert them to a reward-to-risk ratio


2

Example: Multiple Mispriced Assets
Stock WMT VZ GM
Alpha 1.50% -0.50% 0.25%
Beta 0.2095 0.2375 1.6613
Unsystematic Risk 0.0275 0.0215 0.0491
Market Return () 8.00%
Market SD 12.058%
Stock WMT VZ GM
Reward-to-risk: Τ
0.545 -0.233 0.051
40
Example: Multiple Mispriced Assets
➢ Step #2: Sum the reward-to-risk ratios: σ=1=3
2 = 0.545 – 0.233 + 0.051 = 0.364
➢ Weight each asset in the Active Portfolio based on its reward-to-risk ratio as a percentage
of the sum of all reward-to-risk ratios in the Active Portfolio :
➢ Step #3: Calculate the Active Portfolio’s alpha, beta and unsystematic risk: , and
2
= σ=1
=3 = 1.499 × 0.015 – 0.639 × -0.005 + 0.14 × 0.0025 = 0.026
= σ=1
=3 = 1.499 × 0.210 – 0.639 × 0.238 + 0.14 × 1.661 = 0.395

2 = σ=1
=3
2
2 = 1.4992 × 0.0275 + (-0.639)2 × 0.0215 + 0.142 × 0.0491 = 0.0716
Stock WMT VZ GM
Active Portfolio
Weighting
0.545 / 0.364
1= 149.9%
-0.233 / 0.364
2= - 63.9%
0.051 / 0.364
3= 14.0%
41
➢ Step #4: Derive the optimal weight in the Active Portfolio by relating its reward-to-risk to the
market’s reward-to-risk:

0 =
Τ
2
Τ()
2 = ൗ
0.026
0.0716
0.08 −0.02
0.120582
= 0.0882 = 8.82%
➢ Step #5: Adjust for beta: ∗ =

0
1+
0(1−)
=
0.0882
1+0.0882(1−0.395)
= 0.0837 = 8.37%
➢
∗ < 0 because <1: provides more diversification benefit, therefore we slightly
increase the weighting in and slightly decrease the weighting in (from 8.82% to 8.37%)
➢ Therefore, our optimal risky portfolio ∗ would be to put ∗ = 8.37% in the mispriced asset
and 91.63% in the market
Example: Multiple Mispriced Assets
Excel: “Active Portfolio Construction”
42
Performance Measures for
Active Investing
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❑ How can we measure the improved performance from active investing?
❑ The Sharpe ratio of the optimal risky portfolio ∗ resulting from combining with will
exceed that of alone:
∗
2 = 2 +


2
❑ The term

is known as the Information ratio
➢ The contribution of the Active Portfolio () to improving the overall Sharpe ratio depends on
its Information ratio
➢ The Information ratio measures the excess risk and return from security analysis and active
management - potentially resulting in our optimal portfolio ∗ achieving a higher Sharpe
ratio than the market
➢ We will further explore the information ratio in week 8
Sharpe Ratio Improvement
44
Example 1: Sharpe Ratio Improvement
❑ Based on its earlier analysis, Alpha Fund wishes to calculate its potential Sharpe ratio
improvement if its forecasts prove correct
a) Calculate the market Sharpe ratio.
b) Calculate the Information ratio of the active portfolio .
c) Determine the Sharpe ratio of ∗. By how much does it improve?
➢ Market Sharpe ratio: 0.08 −0.02
0.12058
= 0.4976
➢ Active Portfolio Information ratio:

= 0.026
0.0716
= 0.0973
➢ Sharpe ratio of ∗ : ∗
2 = 2 +


2
= 2 + 2 = (0.4976)2 + (0.0973)2 = 0.2571
∗ = 0.2571 = 0.5070 Improvement of 0.5070 – 0.4976 = 0.0094
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❑ Tech Fund outperformed extraordinarily during the period from 2012-2018. The following
table contains summary statistics for Tech Fund against the market:
a) Calculate the and unsystematic risk (expressed as a standard deviation) for Tech Fund.
b) Calculate the market and Tech Fund Sharpe ratios.
c) Calculate the Information ratio for Tech Fund.
d) On an ex-post basis, calculate the optimal weighting in Tech Fund (∗ ) for ∗
e) Determine the Sharpe ratio of ∗. By how much does it improve?
➢ Alpha Tech Fund: = 0.165 − 1.4 × 0.075 = 0.06
➢ Tech Fund unsystematic risk: = 0.302 − 1.42 × 0.1532 = 0.21
Example 2: Sharpe Ratio Improvement
Tech Fund Market
Risk Premium 16.5% 7.5%
Standard Deviation 30.0% 15.3%
Beta 1.4 1.0
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➢ Sharpe ratios: =
0.075
0.153
= 0.49 =
0.165
0.30
= 0.55
➢ Tech Fund Information ratio: =


= 0.06
0.21
= 0.286
➢ Ex-post optimal weighting in Tech Fund:
0 =
Τ
2
Τ()
2 = ൗ
0.06
0.212
0.075
0.1532
= 0.424 = 42.4%
Adjust for beta: ∗ =
0
1+
0 (1−)
=
0.424
1+0.424×(1−1.4)
= 0.511 = 51.1%
➢ Sharpe ratio of ∗ : ∗
2 = 2 +
2
= 2 + 2 = 0.492 + 0.2862 = 0.3219
∗ = 0.3219 = 0.567 Improvement of 0.567 – 0.49 = 0.077
Example 2: Sharpe Ratio Improvement
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❑ BKM Chapter 10 and 13
❑ 5.1 Empirical Testing of Single Index Models
❑ 5.2 Multi-Factor Models
❑ 5.3 Application of Multi-Factor Models
Next Lecture