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# Basic concepts in Finance

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1. A stock has an expected return of 13 percent, its beta is 0.55, and the risk-free rate is 7.15 percent. What must the expected return on the market be?

2. You own a portfolio equally invested in a risk free asset and two stocks. If one of the stocks has a beta of 1 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

3. A stock has an expected return of 11 percent, its beta is 1.3, and the expected return on the market is 9 percent. What must the risk-free rate be? (Do not round your intermediate calculations.)

4. A stock has a beta of 1.15, the expected return on the market is 10 percent, and the risk-free rate is 3.5 percent. What must the expected return on this stock be?

5. A portfolio is invested 15 percent in Stock G, 60 percent in Stock J, and 25 percent in Stock K. The expected returns on these stocks are 8 percent, 20 percent, and 28 percent, respectively. What is the portfolio's expected return?

6. A portfolio has 60 shares of Stock A that sell for \$48 per share and 120 shares of Stock B that sell for \$25 per share.
(a) What is the portfolio weight of Stock A?
(b) What is the portfolio weight of Stock B?

7. You own a stock portfolio invested 25 percent in Stock Q, 20 percent in Stock R, 15 percent in Stock S, and 40 percent in Stock T. The betas for these four stocks are 1.8, 1.36, 1.54, and 0.79, respectively. What is the portfolio beta?

8.State of Economy Probability of State of Economy Rate of Return if State occurs
Recession 0.11 -0.01
Normal 0.35 0.14
Boom 0.54 0.32

Calculate the expected return?

9. You have \$40,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 16 percent and Stock Y with an expected return of 6 percent.

(a) If your goal is to create a portfolio with an expected return of 10.5 percent, how much money will you invest in Stock X?

(b) If your goal is to create a portfolio with an expected return of 10.5 percent, how much money will you invest in Stock Y?

#### Solution Preview

1.A stock has an expected return of 13 percent, its beta is 0.55, and the risk-free rate is 7.15 percent. What must the expected return on the market be?
Market return=rm=?
Beta=b=0.55
Risk free rate=rf=7.15%
Expected return on stock=r=13%
CAPM Model gives us
r=rf+b(rm-rf)
13%=7.15%+0.55*(rm-7.15%)
0.55*(rm-7.15%)=13%-7.15%=0.0585
0.55rm-0.039325=0.0585
rm=(0.0585+0.039325)/0.55=0.177864
rm=17.7864%

2. You own a portfolio equally invested in a risk free asset and two stocks. If one of the stocks has a beta of 1 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

Beta of one stock=1
Weight of one stock=0.5
Beta of second stock=? (say b)
Weight of one stock=0.5
Portfolio beta=1 (Portfolio is as risky as the market)
So,
1=0.5*1+0.5*b
b=1

3. A stock has an expected return of 11 percent, its beta is 1.3, and the expected return on the market is 9 percent. What must the risk-free rate be? (Do not round your intermediate calculations.)

Market ...

#### Solution Summary

There are nine problems. Solution to each problem provides step by step methodology to find out the value of desired parameter/s.

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