L8 - The Capital Asset Pricing Model (CAPM)

Question 1

What is the CAPM?

Answer 1

R_j = R_F + β(R_M − R_F )

R_j= expected return (required rate of return)

R_F= risk-free rate

(R_M-R_F) = the average risk premium for a share (expected return on the market minus the risk-free rate)

β = measure of risk

Question 2

What is the simple calculation for the Required return on a share?

Answer 2

R_j = R_F + (R_P )

Rj= expected return (required rate of return)

R_F= risk-free rate

R_P = risk premium

How big is the risk premium:

• Estimate the risk premium for the an average risk share on the stock market
• multiply this number by a risk-adjustment factor for each individual share

Question 3

Why is past data bad for calculating risk premium?

Answer 3

• Bold assumption that the extra returns received in the past reflect their required returns

Objections :

• Investors in shares in past decades might have been lucky
• We don’t know how many years to look at (in the past 20-30 years you would have had better return on risk-free assets which doesnt make sense - need to look at a longer period)
• There is a debate over whether to use the rate of return on a government bond with a high reputation for repaying its debts or its Treasury bills for the risk-free rate of return –> if im investing for more that 3 months shouldnt i be using gilts

Question 4

What is the market risk premium?

Answer 4

• being taken as 5% but can range from 3-5%
• if you only look back to 2015 we get a negative risk premium which doesnt make sense but the further we go back we get a more accurate real rate of return
• risk free rate is the equities return minus either the treasury bill (short term and what is consider the real risk free rate) or the gilt rate (longer term)

Question 5

What is the US equity risk premium between 1800 and the 2000?

Answer 5

Question 6

Why is it hard to forcast the risk premium?

Answer 6

• there are long run trends over time (its not constant) - ask financial officers from s&p 500 what it would be and they predicted variations between 3 and 5% - Graham & Harvey (2015)
• differs between countries - venezuela and greece have are going through times of political unrest so the s.d. of their risk premium is high so it can vary alot - Fernandez et al. (2016)

Question 7

What does the capital market line look like?

Answer 7

• the umbrella demostrate the different portfolio variations we can have of a set of stocks
• investors would only buy assets on the efficient frontier
• but when risk-free assets are added to portfolio, this creates the capital market line which shows all the combinations of risk-free assets and market portfolios (all assets in the economy) –> normally refer to an index like s&p 500 or FTSE
• as utility increases as we move north west, investors will choose all points on Capital Market Line over the Efficient Frontier as it is completely dominated by it

Question 8

How do you calculated Expected Return and Risk of a model?

Answer 8

• dont need expectaiton operator for the risk-free rate as the return can always be calculated

Question 9

How do you derive the Capital Market Line?

Answer 9

Represent Expected return as a risk of the portfolio

Question 10

What is Systematic and Unsystematic risk?

Answer 10

• Unsystemic risk –> CEO resigning, new patent or contract –> the more shares you have the more this decreases as different shares will by up or down and cancel each other out
• Systemic risk –> changes in monetary policy, changes in taxes, GDP growth, Business cycle

Question 11

What is Beta in CAPM?

Answer 11

The CAPM defined systematic risk as beta.

• Beta (β) measures the covariance between the returns on a particular share with the returns on the market as awhole
• In the CAPM model, because all investors are assumedto hold the market portfolio, an individual asset (e.g. a share) owned by an investor will have a risk that is defined as the amount of risk that it adds to the market portfolio

CAPM also assume that investors hold a well diversified portfolio

Question 12

What is the formula for Beta?

Answer 12

Question 13

How do we interpret the value of beta?

Answer 13

• β = 1 ⇒ A 1 per cent change in the market index return generally leads to a 1 per cent change in the return on a specificshare.
• 0 < β < 1 ⇒ A 1 per cent change in the market index return generally leads to a less than 1 per cent change in the returns on aspecific share.
• β > 1 ⇒ A 1 per cent change in market index return generally leads to a greater return than 1 per cent on a specific company’s share –> riskier share

Question 14

What is the Security Market Line?

Answer 14

R_j = R_F + β(R_M − R_F )

• R_j= expected return (required rate of return)
• R_F= risk-free rate
• (R_M-R_F) = the average risk premium for a share (expected return on the market minus the risk-free rate)
• β = measure of risk
• On the graph we are now measuring risk in terms of β
• a rise in the risk free rate will only shif the line up as the risk free rate used in the calculation for the average risk premium is the long run average so will not be affected by the calculation

Question 15

What is the Characteristic line?

Answer 15

• used to estimate β –> using a regression model referred to as the characterisitc line

R_j = α + β_j(R_M) + e

• Rj= rate of return on the jth share
• R_M= rate of return on the market index portfolio
• α - regression line intercept
• e = residual error about regression line (in this imsple case this has a value of zero becasue all the plot points are on a straight line)
• β_j= the beta of security j

Slope of the characterisitc line is the beta for share j:

β_j = ΔR_j/ΔR_M

Recall that:

R_j = R_F + β_j(R_M − R_F )

therefore:

α= (1-β_j )R_F

Question 16

What does the characteristic line look like with and without unsystematic risk?

Answer 16

• with no unsystematic risk all shares would lie on the characteristic line
• once introduced, different shares would have different returns compared to the market, thus the characteristic line here is a best fit of the portfolios
• up to the line describe systematic risks, deviations from this is caused by unsystematic risk

Question 17

What are the Application of the CAPM model?

Answer 17

• Investment in the financial markets
  
  • Portfolio selection –> risk adverse (low beta), or want those that are highly correlated in order to benefit from market moves
  • Mispriced shares –> to identify anomalous risk-return characteristic shares, (buy thoses where beta seems to low for its returns and sell those that the returns are suboptimal for the beta)
  • Measuring portfolio performance
    
    • Treynor’s ratio –> return above the risk free rate/ beta observe return per unit of beta risk)
    • Sharpe’s ratio –> return above the risk-free rate divided by standard deviation
• Calculating the required rate of return on a firm’s investment projects

Question 18

What are the accepted and controverisal aspect of the CAPM?

Answer 18

Accepted

• Shareholders demand a higher return for riskier assets • Risk-averters are wise to diversify
• The risk of securities (for example shares) has two elements:
  
  • (a) unsystematic risk factors specific to firms which can be diversified away; and
  • (b) systematic risk caused by risk factors common to all firms
• Investors will not be rewarded for bearing unsystematic risk
• Different shares have different degrees of sensitivity to the systematic risk elements

Controversial

• Systematic risk is measured by beta which, in practice,is calculated as the degree of co-movement of a security’s return with a market index return
• Beta, as calculated by examining past returns, is valid for decision making concerned about the future

Question 19

What is the issue with measuring beta eith the CAPM model?

Answer 19

• not clear whether it is more appropriate to use daily, weekly or monthly data, or whether the observation period should be three, five or ten years
• . Historical betas of Coca-Cola. Betas calculated each day of April 2009 with respect to the S&P 500 index (the main US share index) using 5 years of monthly, weekly and daily data (top) –> very different values of beta
• Historical betas of Walt Disney, Walmart and Coca-Cola. Betas calculated each day of April 2009 with respect to the S&P 500 using 5 yearsof monthly data. (bottom) –> beta changes over time

Question 20

What are some technical problem with CAPM?

Answer 20

• Ex-ante theory with ex-post testing
• The market portfolio is unobtainable
• One-period model
• Very few government securities are close to being risk free
• Unrealistic assumptions:
  
  • Investors are rational utility maximizers
  • Information is freely available
  • Investors can borrow and lend at the risk free-rate
  • Capital markets are perfectly competitive and frictionless
  • Securities are infinitely divisible

Question 21

What was the summary of early empirical work on the CAPM?

Answer 21

• the intercept or return on a just risk free asset is higher than the theoretical Secuities Market line anticipated
• the SML was also flatter implying that shares with a lower level of risk actually offered higher levels of return, and those with higher levels of risk were actually getting lower levels of return
• when testing r-squared ( seeing how much information on returns on a asset is explained by CAPM) –> it was really small meaning that there were other factors that were affecting the return

Question 22

According to Barclays (2016) what is the average return of the most common assets?

Answer 22

equities - 5%

gilts - 1.3%

cash - 0.8%

• more return you have the larger the standard deviation of the asset’s returns will be - high risk