L8 - CAPM II

Question 1

What happens to CAPM when we put restrictions on borrowing?

Answer 1

• Every portfolio on the efficient frontier, except for the global minimum-variance portfolio, has a “companion” portfolio on the bottom (inefficient) half of the frontier that is completely uncorrelated with
• Because it is uncorrelated, the companion portfolio is referred to as the zero-beta portfolio of the efficient portfolio
• The market portfolio is efficient, so it has zero covariance with a particular frontier portfolio z.
  
  • these companion portfolios can be seen as playing the same role as risk free asset
• Without borrowing –> people have to invest on the Efficient Frontier and thus have to accept higher risk per unit of return –> without the CML
  
  • • Restrictions on borrowing leads to a flatter SML as the only was to increase their returns from the Market Portfolio is to invest in high beta stocks
      
      • invest in more higher beta stocks(but demand for them is higher and we reduce their value and return)
      • This is why the SML is flatter
• This is the zero-beta CAPM. Instead of the risk free rate, rf , in the CAPM equation we have the expected rate of return on a portfolio that has zero covariance with the market portfolio.
• Investors who would otherwise wish to borrow and leverage their portfolios but who find it impossible or costly will instead tilt their portfolios toward high-beta stocks and away from low-beta ones.
• As a result, prices of high beta stocks will rise, and their risk premiums will fall. The SML will be flatter than in the simple CAPM
  
  • Risk premium for low beta will also rise causing it to be flatter​
    
    • imagine the SML going through the return of the companion portfolio at the axis

Question 2

What are some other extensions of CAPM?

Answer 2

• An intertemporal model (ICAPM)
• Multiple risk factors
  
  • Fama French –> are there other factors that can explain the alpha that isn’t related to CAPM
• A consumption-based model (CCAPM)
• Incorporation of non-traded assets such as labour or human capital.
  
  • the assumption we make during CAPM is that all assets are traded in the economy
  • but we don’t trade human capital –> what if we considered the PV of future wage income compared to the dividend paid in an economy we know the formers is much larger
  • don’t trade private asset
    
    • hedge against the risk they may have –> hedge in an investment beta different to their company
  • risk of losing your job or wage decrease –> use the investment to hedge this risk by investing in more labour-intensive companies
    
    • when wages drop they are going to benefit as their costs have suddenly dropped - high profit, higher dividend
• Non-constant beta (conditional CAPM)
• CAPM modified for liquidity risk.
  
  • want larger return for less liquid securities

Question 3

What is the ICAPM?

Answer 3

An intertemporal model (ICAPM)

• CAPM is static - it doesn’t link to how it will affect their decisions in the future
• are there another risk than market risk –> will beta, interest rates, inflation (which would affect PV) change in the future
• The investor need to consider all current and future uncertainties (demand higher return now given more future risks)
• Select securities with a strong correlation with the interest rate

Question 4

What is the consumption-based CAPM?

Answer 4

A consumption-based model (CCAPM)

• all this investing is to allow them to achieve a higher standard of living and to smooth their consumption (and living standard) over time
• this means the nature of risk changes –> no longer related to market risk but how it relates to consumers consumption level
• how do you value security i with a high return during a time when consumption is high (e.g. in economic boom) –> value it less as it is risky, only need it in times consumption is low
• security will command a high return if correlated with our consumption is positive and high (we have less demand when cash is low) –> and lower return when it is inversely correlated with consumption level (appreciate the fact they pay us the most when consumption is low)
• An asset is riskier in the CCAPM if it pays less when consumption is low and savings are high –> if I saving a lot I want it to be paying me more, need extra risk premium
  
  • when we retire income drops so we need to save for our retirement so we would like to invest in securities that pay good cash dividend when our consumption is lower

Question 5

How can you derive CAPM from the Single-Index market model?

Answer 5

• As n tends towards the infinite risk of portfolio tends to zero –> if w = 1/n (equally weighted)
• Investors can diversify the non-systematic risk and by choosing stocks with positive alpha can increase the risk premium on Q.
• However, if investors pursue positive alpha stocks, prices of positive alpha stocks will rise and prices of negative alpha stocks will fall.
• This will continue until all alpha values are driven to zero.
• At this point, investors will be content to minimize risk by completely eliminating unique risk, that is, by holding the broadest possible, market portfolio.
• When all stocks have zero alphas, the market portfolio is the optimal risky portfolio.

Question 6

How can we test CAPM?

Answer 6

• Test the theory that all securities should lie on the Security Market Line

Question 7

How do you construct the market portfolio?

Answer 7

• this also called a value weighted portfolio
  
  • good thing about these types of portfolios is that the weight doesn’t change as price changes as the price is a part of both the numerator and denominator

Question 8

What can we use as a proxy for the market index?

Answer 8

• The S&P500 is an index that represents a value-weighted portfolio of 500 of the largest U.S. stocks. It represents almost 80% of the U.S. stock market in terms of market capitalization.
• Wilshire 5000, provide a value-weighted index of all U.S. stocks listed on the major stock exchanges
• Dow Jones Industrial Average (DJIA), which consists of a portfolio of 30 large industrial stocks. The DJIA is a price-weighted (rather than value-weighted) portfolio. A price-weighted portfolio holds an equal number of shares of each stock, independent of their size.
• FTSE 100 which is a value-weighted portfolio of the 100 largest UK stocks.

Question 9

Historical Excess Returns of the S&P compared to 1 and 10 year treasury bonds?

Answer 9

Question 10

How do you estimate beta?

Answer 10

Jensen’s alpha –> In finance, Jensen’s alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance instead of a market index. The security could be any asset, such as stocks, bonds, or derivatives

Question 11

How do you formally test CAPM using regressions?

Answer 11

• Second-pass
  
  • the average excess return for each individual security regressed on the beta of the security and its variance

Question 12

When testing CAPM against the NYSE, what were some early findings?

Answer 12

• η1 –> is a lot lower than the average market risk premium
• η0 is 0

Question 13

What are the reasons the empirical test of CAPM could have failed?

Answer 13

• Stock returns are very volatile. S.D of returns of stocks in S&P500 is about 40% –> makes the estimation inaccurate
• Market index is not Market portfolio.
• Betas estimated in the first stage are with errors. Extending the time period also doesn’t help as betas change over time.
• One solution to overcome the betas estimation error is to group securities into portfolios.
  
  • rank them by their betas then during the second pass regression we group them by quartiles or quintiles and then perform the regression
• To achieve the largest possible dispersion of beta coefficients for the second stage, first rank the stocks by betas and then group them into portfolios.