INVESTMENT PLANNING
LECTURE 17: CAPM & OTHER MODELS
MARCH 16, 2015
Vandana Srivastava
Review of CAPM-- CML

efficient frontier (the straight line through rf and T) is the same for every
investor (CML)
Two fund separation:
 every investor allocates his wealth between two portfolios: the riskfree asset and the Tangency portfolio T(or m)
In equilibrium, all risky assets must belong to T
for every asset, the weight in T must be the same as in the whole market

CML:

CML is applicable only to an investor’s final (combined) portfolio



 E (rm )  r f
E (rp )  r f  
 m

 p

https://www.math.ust.hk/~maykwok/courses/ma362/Topic2.pdf
Review of CAPM-- Security Market Line

is essentially a graph
representation of CAPM
formula
plots the expected return of
stocks on the y-axis, against
beta on the x-axis
 intercept is the risk free rate
and the slope represents the
market premium
 SML is applicable to any
security, asset or portfolio

E (r j )  r f   j ( E (rm )  r f )
Deductions from SML

efficient portfolios lie on both CML and SML

All correctly priced assets lie on the SML in equilibrium


If an asset is overpriced / overvalued it will lie below the SML since it
will provide an expected return less than what is determined by the
SML given its risk (beta)
If an asset is underpriced / undervalued it will lie above the SML
since its expected return will be greater than what the SML determines


Investors will flock to buy it, driving up its price and pushing its expected
return down to the SML.
By estimating a SML and plotting an asset, the investor can determine
whether the asset is over or underpriced and make investment
decisions
http://economics.fundamentalfinance.com/capm.php
Example: Overpriced / Underpriced Security


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

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current risk-free rate is 5%
market is expected to return 12% next year
beta of the security is 1.9
Expected return = 5% + 1.9*(12% - 5%) = 18.3%
We expect the asset to return 18.3% and be
plotted on the SML
current real rate of return for the asset is 19%.
The asset would be plotted above the SML.
Therefore, it is undervalued and should be bought
Example: Overpriced / Underpriced Security

A particular stock sells for $30. The stock’s beta is 1.25, the riskfree rate is 4%, and the expected return on the market portfolio is
10%. If forecast is that the stock will be worth $33 next year
(assume no dividends), should you buy the stock or not?
Solution:
R = Rf + B(Rm – Rf)
= 4 + 1.25 (10 – 4) = 11.5%
Return on the stock: (33-30)/30 = 10%.
Don’t buy the stock. You expect a return of 10%. The stock should
return 11.5%, according to CAPM.
Arbitrage Pricing Theory (APT)



developed by Stephen Ross (1976)
considered as alternative of CAPM method for measuring risk
arbitrage opportunity:


if investors can invest risklessly and earn more than the riskless rate
premise of the model:

if 2 portfolios have the same risk exposure but different expected
return


investors will buy portfolio with high expected return and sell portfolio with
lower expected return and earn the difference as riskless profit
to prevent arbitrage from taking place, both portfolios should earn
the same return
https://www.academia.edu/6549296/Describe_the_Arbitrage_Pricing_Theory_APT_model
Arbitrage Pricing Theory (APT)
https://www.academia.edu/6549296/Describe_the_Arbitrage_Pricing_Theory_APT_model
Fama-French 3 Factor Model


used to explain differences in the returns of diversified equity
portfolios
started with the observation that two classes of stocks have
tended to do better than the market as a whole:


small caps
stocks with a low Price-to-Book ratio (P/B, customarily called value stocks,
contrasted with growth stocks)
• r is the portfolio's expected rate of return, rf is the risk-free return rate, and rm is the
return of the market portfolio
• SMB stands for "Small [market capitalization] Minus Big" and HML for "High [book-tomarket ratio] Minus Low"; they measure the historic excess returns of small caps over big
caps and of value stocks over growth stocks.
Estimating “Beta” in CAPM
Step 1: use past return data to compute a historical beta as proxy for the
true “future” beta
Step 2: Use approximation to the market portfolio. Choose SENSEX or Nifty
as a proxy for market portfolio, m
Step 3: Choose a time period for calculations
Step 4: Perform the following regression
R j  ˆ  ˆ j Rm   j ..........................(1)
For SML,
R j  r f  ˆ  ˆ j ( Rm  r f )   j ..........................(2)
(1) is a good approximat ion of (2) if ˆ  0
Interpretation of Regression in Excel
•The standard error is an estimate of
the standard deviation of the coefficient
• can be thought of as a measure of the
precision with which the regression
coefficient is measured
sqrt(R)
R Square
R Square equals 0.962, which is a very good fit.
96% of the variation in Quantity Sold is
explained by the independent variables Price
and Advertising. The closer to 1, the better the
regression line (read on) fits the data.
http://www.excel-easy.com/examples/regression.html
Interpretation of Regression in Excel
Significance F and P-values
To check if your results are reliable (statistically significant), look at Significance F (2.14561E-09 )
If this value is less than 0.05, it is OK. If Significance F is greater than 0.05, it's probably better to stop
using this set of independent variables. Delete a variable with a high P-value (greater than 0.05) and rerun
the regression until Significance F drops below 0.05.
Most or all P-values should be below 0.05. In this example p-value is(2.15E-09).
Interpretation of Regression in Excel
t-statistic
The t statistic is the coefficient divided by its standard error
Coefficients
The regression line is:
•For IBM:
Example: Estimating “Beta” in CAPM

For IBM:
 Estimated
beta for IBM is 1.0923 and its standard error is
.1547 or 15.47%
 at 95% confidence interval


Pr ob ˆ  2ˆ ˆ   true  ˆ  2ˆ ˆ  0.95
Pr ob1.0923  2(0.1547)   true  1.0923  2(0.1547) 
Pr ob.7828   true  1.4018  0.95
Confidence interval from regression is given by {.7828, 1.4018}