Portfolio theory and the capital asset pricing model CAPM Flashcards
The measurement of risk
• Risk is measured by the standard deviation of the returns on a share, based on either historical returns or expected future returns
The concept of diversification
- Total risk can be divided into systematic and unsystematic risk.
- Systematic risk is due to systematic factors such as changes in interest rates, business cycles and government policy.
- Unsystematic risk is specific to a given share.
- Unsystematic risk decreases as the number of investments in a portfolio increases: this is called portfolio diversification of risk
Diversification of risk
- Total risk falls as number of investments rises
- The amount of risk diversification depends on correlation between returns and hence on the value of the correlation coefficient (CC).
The two-share portfolio 4
Share S – Mean return: 5.96% – Standard deviation: 8.16% Share T – Mean return: 9.10% – Standard deviation: 13.39%
- Investors can choose portfolios anywhere along the arc SABCDT.
- The risk of these portfolios is less than that represented by the straight line ST.
- Combining S and T has reduced total risk by diversifying unsystematic risk.
- As we increase the number of shares in the portfolio, we obtain a ‘bat-wing’ shape as shown in the next diagram
Portfolio theory 3
- Rational investors invest only on the efficient frontier, thereby maximising their utility.
- If risk-free assets are available, investors will combine them with the market portfolio.
- Rational investors then therefore select their optimal portfolio on the capital market line at a point of tangency with their utility curves.
• Problems with using portfolio theory: 4
- borrowing at the risk-free rate
- identifying the market portfolio
- constructing the market portfolio
- changing composition of market portfolio.
CAPM 4
- The CAPM is a method of share valuation developed by William Sharpe in 1964.
- It is based on a linear relationship between risk and return.
- It is a development of portfolio theory.
- It considers that systematic risk is the only relevant risk when valuing shares.
CAPM assumptions 7
- Investors are rational utility maximisers.
- Information is freely available.
- All investors have similar expectations.
- Investors can borrow and lend at the risk free-rate.
- Investors hold diversified portfolios, thereby eliminating all unsystematic risk.
Capital markets are perfect:
– no taxes or transaction costs
– free entry and exit
– many buyers and sellers
– information is costless and freely available.
Single period transaction horizon
– returns are calculated over a standard period
– usually taken as 1 year.
CAPM components 4
- Return of the market (Rm)
- Risk-free rate of return (Rf )
- Equity risk premium (Rm – Rf )
- Beta value of ordinary shares of a company (βj ).
Meaning of beta
• Beta is seen as an ‘index of responsiveness’ of changes in a security’s returns relative to changes in returns on the market.
Risk-free rate (Rf ) 4
- No assets are totally risk-free, but bonds issued by governments of stable countries are seen as almost risk-free.
- Rf approximated by the yield to maturity of treasury bills (short-term government debt).
- Short maturity as these have lowest risk.
- Current yield (November 2009) is about 2%.
Implications of the CAPM 4
- Investors will require compensation only for systematic risk, since unsystematic risk can be eradicated by portfolio diversification.
- Securities with high levels of systematic risk should, on average, yield high rates of return.
- There should be a linear relationship between systematic risk and return.
- Correctly priced securities should plot on the security market line (SML)
So is the CAPM useful? 5
- A theory should be judged on its performance rather than on its assumptions.
- Portfolio betas are relatively stable.
- Strong evidence on validity of security market line has now given way to doubts.
- Is there a better alternative to the CAPM?
- Perhaps multivariate models such as APM (Arbitrage Pricing Model)?
