1. INVESTMENT PLANNING LECTURE 17: CAPM & OTHER MODELS MARCH 16, 2015 Vandana Srivastava

2. Review of CAPM-- CML  efficient frontier (the straight line through r f and T) is the same for every investor (CML)  Two fund separation:  every investor allocates his wealth between two portfolios: the risk- free 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 https://www.math.ust.hk/~maykwok/courses/ma362/Topic2.pdf

3. 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

4. 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

5. Example: Overpriced / Underpriced Security  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

6. Example: Overpriced / Underpriced Security  A particular stock sells for $30. The stock’s beta is 1.25, the risk- free 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.

7. 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

8. Arbitrage Pricing Theory (APT) https://www.academia.edu/6549296/Describe_the_Arbitrage_Pricing_Theory_APT_model

9. 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, r f is the risk-free return rate, and r m is the return of the market portfolio SMB stands for "Small [market capitalization] Minus Big" and HML for "High [book-to- market ratio] Minus Low"; they measure the historic excess returns of small caps over big caps and of value stocks over growth stocks.

10. 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

11. Interpretation of Regression in Excel 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 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)

12. 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).

13. Interpretation of Regression in Excel t-statistic The t statistic is the coefficient divided by its standard error Coefficients The regression line is:

14. 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 Confidence interval from regression is given by {.7828, 1.4018} For IBM: