# Finance Question: Beta and Risk

You are working as an intern at Coral Gables Products, a privately owned manufacturing

company. You got into a discussion with the Chief Financial Officer (CFO) at Coral Gables

about weighted average cost of capital calculations. She pointed out that, just as the beta

of the assets of a firm equals a weighted average of the betas for the individual assets (as

shown below):

Bn Asset Portfolio = SUM_(t - 1, n) xiBi = x1B1 + x2B2 + ... + xnBn

The beta of the assets of a firm also equals a weighted average of the betas for the debt, preferred stock, and common stock of a firm:

Bn Asset Portfolio = SUM_(i = 1, n) xiBi = x_Debt * B_debt + x_ps * B_ps + x_cs * B_cs

a) Why must this be true? Please provide your explanation with appropriate examples.

b) Discuss your understanding of WACC and explain how the individual cost of each capital component (equity, preference and debt capital) can be calculated.

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#### Solution Preview

a. Betas measure risk relative to market risk. It ranges from 0 to 1. When beta is zero for an asset there is no risk associated with this asset and hence expected return is not high. When beta is one, the risk associated with the asset is highest and hence expected return is high. For an investor goal is to collect a large number of assets and form a portfolio to minimize risk with deterministic rate of return. Hence, for a portfolio, beta is equal to weighted average of betas for the individual assets.

For example a portfolio consists of three stocks with betas 0.8, 0.6, and 0.4. These ...

#### Solution Summary

Finance questions about beta and risks for Coral Gables Products are examined.

Finance Questions and Problems

1. The probability distribution of a less risky return is more peaked than that of a riskier return. What Shape would the probability distribution have for (a) completely certain returns and (b) completely uncertain return?

2. Suppose you owned a portfolio consisting of $250,000 of US gov bonds with a maturity of 30 years

a.would your portfolio be riskless?

b.now suppose you hold a portfolio consisting of $250,000 of 30 day treasury bills. Every 30 days your bills mature, and you reinvest the principal in a new batch of bills

is your portfolio truly risk less?

3. If a company beta were to double, would its expected return double?

4. In the real world,is it possible to construct a portfolio of stocks that has an expected return equal to the risk-free rate?

5.An individual has $35,000 invested in a stock with a bet of 0.8 and another $40,000 invested in a stock with a beta 1.4. If these are the only two investments in her portfolio, what is her portfolio beta

6. Assume that the risk rate is 6% and that the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7

7. The market and stock j have the following probability distributions

probability Rm rj

0.3 15% 20%

0.4 9 5

0.4 18 12

a- calculate the expected rates of return for the market and stock j

b-calculate the standard deviations for the market and stock j

c-calculate the coefficients of variations for the market and stock j

8. Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolios beta is 1.12. Now, suppose you sell one of the stocks with a beta of 1.0 for $7,500 and use the proceeds to buy another stock whose beta is 1.75. Calculate the new beta of the portfolio.

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