## Efficient Risk Taking

In the capital asset pricing model, the most efficient way to take a lot of risk is to a. Buy a well-balanced portfolio of the riskiest stocks in the market b. Buy risky stocks that are also undervalued c. Borrow money and buy a well diversified portfolio

### 3. Measuring the Market Risk of an Individual Asset

The risk of any asset to an investor is the risk added on by that asset to the investor's overall portfolio. In the CAPM world, where all investors hold the market portfolio, the risk of an individual asset to an investor will be the risk that this asset adds on to the market portfolio. Intuitively, assets that move more with the market portfolio will tend to be riskier than assets that move less, since the movements that are unrelated to the market portfolio will not affect the overall value of the portfolio when an asset is added on to the portfolio. Statistically, this added risk is measured by the covariance of the asset with the market portfolio.

The covariance is a non-standardized measure of market risk; knowing that the covariance of Disney with the Market Portfolio is 55% does not provide a clue as to whether Disney is riskier or safer than the average asset. We therefore standardize the risk measure by dividing the covariance of each asset with the market portfolio by the variance of the market portfolio. This yields the beta of the asset:

_ . Covariance of asset i with Market Portfolio

Variance of the Market Portfolio

Since the covariance of the market portfolio with itself is its variance, the beta of the market portfolio, and by extension, the average asset in it, is one. Assets that are riskier than average (using this measure of risk) will have betas that exceed one and assets that are safer than average will have betas that are lower than one . The riskless asset will have a beta of zero.

### 4. Getting Expected Returns

The fact that every investor holds some combination of the riskless asset and the market portfolio leads to the next conclusion, which is that the expected return on an asset is linearly related to the beta of the asset. In particular, the expected return on an asset can be written as a function of the risk-free rate and the beta of that asset; Expected Return on asset i = Rf + Pi [E(Rm) - Rf]

= Risk-free rate + Beta of asset i * (Risk premium on market portfolio) where,

E(Ri) = Expected Return on asset i Rf = Risk-free Rate

E(Rm) = Expected Return on market portfolio Pi = Beta of asset i

To use the capital asset pricing model, we need three inputs. While we will look at the estimation process in far more detail in the next chapter, each of these inputs is estimated as follows:

• The riskless asset is defined to be an asset where the investor knows the expected return with certainty for the time horizon of the analysis. Consequently, the riskless rate used will vary depending upon whether the time period for the expected return is one year, five years or ten years.

Beta: The beta of any investment in the CAPM is a standardized measure of the risk that it adds to the market portfolio.

• The risk premium is the premium demanded by investors for investing in the market portfolio, which includes all risky assets in the market, instead of investing in a riskless asset. Thus, it does not relate to any individual risky asset but to risky assets as a class.

• The beta, which we defined to be the covariance of the asset divided by the market portfolio, is the only firm-specific input in this equation. In other words, the only reason two investments have different expected returns in the capital asset pricing model is because they have different betas.

In summary, in the capital asset pricing model all of the market risk is captured in one beta, measured relative to a market portfolio, which at least in theory should include all traded assets in the market place held in proportion to their market value.

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