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8-2 The Relationship between Risk and Return ​

recap

  • treasury bills = least risky investment
  • = treasury bills have a beta of 0.
  • the beta of a portfolio of common stocks is 1.0.

market risk premium

the difference between the return on the market and the interest rate.

mrp=rm−rf it has averaged 7.7% since 1900. if we add back the average interest rate of 5.5%: market return has had an average of 12.7%

CAPM

the capital asset pricing model states that the expected risk premium on each investment is proportional to it's beta. This means that each investment should lie on the sloping security market line connecting treasury bills and the market portfolio.

Expected risk premium on stock=β⋅expected risk premium on marketr−rf=β(rm−rf)

CAPM review

  1. Investors like high expected return and low standard deviation. Common stock portfolios that offer the highest expected return for a given standard deviation are known as efficient portfolios.
  2. If the investor can lend or borrow at the risk free rate of interest, one efficient portfolio is better than all the others. The portfolio that offers the highest ratio of risk premium to standard deviation. A risk averse investor will put part of his money in the risk free asset. A risk tolerant investor will put all her money in a this portfolio or may borrow and put in even more.
  3. If no one has any superior info each investor should should hold the market portfolio (ex. s&p 500 index fund)
  4. Do not look at the risk of a stock in isolation but at its contribution to portfolio risk, This contribution depends on how sensitivity of the stock to changes in the value of the portfolio.
  5. A stock's sensitivity to changes in the value of the market portfolio is known as beta. Beta, therefore measures the marginal contribution of a stock to the risk of the market portfolio.

Every stock must lie on the security market line because:

  • no investor would invest under the line.
  • all stocks together = market portfolio stocks on average lie on the line, so there can be no stocks above the line, since there are no stocks below.