FIN 315 Final

Suppose you observe the following situation: Security. Beta. Expected Return A 1.16 .1137 B .92 .0984 Assume these securities are correctly priced. Based on the CAPM, what is the return on the market?

10.35%

The common stock of Flavorful Teas has an expected return of 21.42 percent. The return on the market is 15 percent and the risk-free rate of return is 4.3 percent. What is the beta of this stock?

21.42 = 4.3 + B*(15 - 4.3) Beta =1.6

Standard deviation measures which type of risk?

Total

You own 330 shares of Stock X at a price of $23 per share, 200 shares of Stock Y at a price of $46 per share, and 265 shares of Stock Z at a price of $69 per share. What is the portfolio weight of Stock Y?

= 0.2623

The risk-free rate of return is 2.7 percent, the inflation rate is 3.1 percent, and the market risk premium is 6.9 percent. What is the expected rate of return on a stock with a beta of 1.08?

According to the question: Risk-free rate of return = 2.7% Inflation rate = 3.1% market risk premium = 6.9 % Beta= 1.08 Expected Return=2.7%+(1.08×6.9%) =0.101520000000000260 Expected Return = 10.152%

The common stock of Jensen Shipping has an expected return of 15.4 percent. The return on the market is 11.2 percent, the inflation rate is 3.1 percent, and the risk-free rate of return is 3.6 percent. What is the beta of this stock?

As per capital asset pricing model, Re = Rf + (Rm - Rf) x Beta Where, Re = Expected rate of return = 15.4 Rf = Risk Rf = Riskfree rate of return = 3.6 Rm = Return on market = 11.2 Beta = Beta of the stock So, putting these values in above equation we get 15.4 = 3.6 + (11.2 - 3.6) x Beta So, Beta = (15.4 - 3.6) / 7.6 = 1.55

You have a portfolio that is 32 percent invested in Stock R, 14 percent invested in Stock S, with the remainder in Stock T. The expected return on these stocks is 8.3 percent, 9.7 percent, and 12.0 percent, respectively. What is the expected return on the portfolio?

Asset Weight Return Weight * Return R 32.00% 8.30% 2.66% S 14.00% 9.70% 1.36% T 54.00% 12.00% 6.48% 100.00% 10.49% Expected Return =10.49%

The stock of Big Joe's has a beta of 1.54 and an expected return of 12.80 percent. The risk-free rate of return is 5.3 percent. What is the expected return on the market?

Expected return on the market=r−Rf/b+Rf Where; r = Expected return 0.1280 b = Beta 1.54 Rf = Risk free rate 0.053 Expected return on the market=0.1280−0.053/1.54+0.053= 0.1017 Expected return on the market = 0.1017 or 10.17%

A portfolio consists of $13,400 in Stock M and $18,900 invested in Stock N. The expected return on these stocks is 8.50 percent and 11.60 percent, respectively. What is the expected return on the portfolio?

Total Portfolio Value = Invested in stock M + Invested in stock N Total Portfolio Value = $13,400 + $18,900 Total Portfolio Value = $32,300 To Calculate Expected Return of Portfolio- Expected Return = Expected Return of stock M * (Invested in Stock M / Total Portfolio Value) + Expected Return of stock N * (Invested in stock N / Total Portfolio Value) Expected Return = 0.085 * ($13,400 / $32,300) + 0.1160 * ($18,900 / $32,300) Expected Return = 0.0352 + 0.0679 Expected Return = 10.31%

The expected return on a stock computed using economic probabilities is:

a mathematical expectation based on a weighted average and not an actual anticipated outcome.

You have a portfolio that is equally invested in Stock F with a beta of .99, Stock G with a beta of 1.41, and the market. What is the beta of your portfolio?

Beta of Stock F = 0.99 Beta of Stock Beta of StockG = 1.41 Beta of Market Beta of Market= 1 As you have invested equally in each of the three which is 33.33% Calculating the Beta of Portfolio:- Beta of Portfolio = (Beta of Stock F)(Weight of Stock F) + (Beta of Stock G)(Weight of Stock G) + (Beta of Market)(Weight of Market) Beta of Portfolio = (0.99)(0.3333) + (1.41)(0.3333) + (1)(0.3333) Beta of Portfolio = 0.329967 + 0.469953 + 0.3333 Beta of Portfolio = 1.13

You own a portfolio that has a total value of $140,000 and a beta of 1.30. You have another $55,000 to invest and you would like the beta of your portfolio to decrease to 1.11. What does the beta of the new investment have to be in order to accomplish this?

Existing investment (EI) = $140,000 New investment (NI) = $55,000 Total investment (TI) = $195,000 (i.e. $140,000 + $55,000) Beta of existing investment (EB) = 1.30 Beta of overall new portfolio (PB) = 1.11 Beta of new investment (NB) = ? Explanation: We will use weighted beta formula. Step 2/2 Calculation of the Beta of new investment (NB); Formula; NB=(PB−EB×EI/TI)×TI/NI NB=(1.11−1.30×140,000/195,000)×195,000/55,000=0.626 = 0.626.

Consider the following information: State of Probability of State Rate of Return Economy of Economy if State Occurs Stock A Stock B Recession. .04 .097 .102 Normal .72 .114 .133 Boom .24 .156 .148 The market risk premium is 7.4 percent, and the risk-free rate is 3.1 percent. The beta of Stock A is ________ and the beta of Stock B is ________.

Expected return = (0.04 * 0.097) + (0.72 * 0.114) + (0.24 * 0.156) Expected return = 0.00388 + 0.08208 + 0.03744 = 0.1234 As per CAPM, Expected or required Expected or required return = Risk free rate + Beta * Market risk premium Putting the given values in the above formula, we get, 0.1234 = 3.1% + Beta * 7.4% 0.1234 = 0.031 + Beta * 0.074 0.1234 - 0.031 = Beta * 0.074 0.0924 = Beta * 0.074 Beta = 0.019752 / 0.074 Beta = 1.25 Stock B: Expected return = (0.04 * 0.102) + (0.72 * 0.133) + (0.24 * 0.148) Expected return = 0.00408 + 0.09576 + 0.03552 = 0.13536 As per CAPM equation, 0.13536 = 3.1% + Beta * 7.4% 0.13536 = 0.031 + Beta * 0.074 0.13536 - 0.031 = Beta * 0.074 0.10436 = Beta * 0.074 Beta = 0.10436 / 0.074 = 1.41 = 1.25; 1.41

What is the standard deviation of the returns on a portfolio that is invested 37 percent in Stock Q and 63 percent in Stock R? State of Probability of Rate of Return Economy State of Economy if State Occurs Stock Q Stock R Boom .15 .16 .15 Normal .85 .09 .13

Expected return of Q= probability * return = 0.15 * 16% + 0.85 * 9% = 2.4% + 7.65% = 10.05% Expected return of R= probability * return = 0.15 * 15% + 0.85 * 13% = 2.25% + 11.05% = 13.30% Standard deviation of Q = √ probability * (return - expected return)^2 = √ 0.15 * (0.16 - 0.1005)^2 + 0.85 * (0.09 - 0.1005)^2 = √ 0.15 * (0.0595)^2 + 0.85 * (-0.0105)^2 = √ 0.15 * (0.00354025) + 0.85 * (0.00011025) = √ 0.0005310375 + 0.0000937125 = √ 0.00062475 = 0.024995 or 2.4995% Standard deviation of R= √ probability * (return - expected return)^2 = √ 0.15 * (0.15 - 0.1330)^2 + 0.85 * (0.13 - 0.1330)^2 = √ 0.15 * (0.0170)^2 + 0.85 * (-0.0030)^2 = √ 0.15 * (0.000289) + 0.85 * (0.000009) = √ 0.00004335 + 0.00000765 = √ 0.0000051 = 0.007141 or 0.7141% Covariance= probability * (return of A - expected return of A) (return of C - expected return of C) = 0.15 * (16% - 10.05%) (15% - 13.30%) + 0.85 * (9% - 10.05%) (13% - 13.30%) = 0.15 * (5.95%) (1.70%) + 0.85 (-1.05%) (-0.30%) = 1.51725 + 0.26775 = 1.785 or 0.0001785 Standard deviation of portfolio = √ (weight of Q)^2 * (std deviation of Q)^2 + (weight of R)^2 + (std deviation of R)^2 + 2 * weight of Q * weight of R * Covariance = √ (0.37)^2 * (0.024995)^2 + (0.63)^2 * (0.007141)^2 + 2 * 0.37 * 0.63 * 0.0001785 = √ (0.1369) * (0.00062475) + (0.3969) * (0.0000509939) + 0.0000832167 = √ 0.0000855283 + 0.0000202395 + 0.0000832167 = √ 0.0001889845 = 0.0137 or 1.37%

You decide to invest in a portfolio consisting of 25 percent Stock A, 25 percent Stock B, and the remainder in Stock C. Based on the following information, what is the expected return of your portfolio? State of Probability Return if Economy of State of Economy State Occurs Stock A Stock B Stock C Recession .18 -16.2% -2.6% -21.5% Normal .54 12.4% 7.2% 15.8% Boom .28 26.0% 14.5% 30.4%

Expected return of Stock A = 0.18 * (-0.162) + 0.54 * 0.124 + 0.28 * 0.26 = 0.1106 Expected return of Stock B = 0.18 * (-0.026) + 0.54 * 0.072 + 0.28 * 0.145 = 0.0748 Expected return of Stock C = 0.18 * (-0.215) + 0.54 * 0.158 + 0.28 * 0.304 = 0.13174 The expected return of the portfolio = 0.25 * 0.11498 + 0.25 * 0.07679 + 0.5 * 0.14013 The expected return of the portfolio = The expected return of the portfolio = 11.22%

The expected return on a portfolio: I. can never exceed the expected return of the best performing security in the portfolio. II. must be equal to or greater than the expected return of the worst performing security in the portfolio. III. is independent of the unsystematic risks of the individual securities held in the portfolio. IV. is independent of the allocation of the portfolio amongst individual securities.

Expected return of portfolio is a weighted average of stock's return in the portfolio. Thus, Expected return of Portfolio always lies between best performing security's return and worst performing security's return. Risk of individual securities in the portfolio is not used to computed the expected return of portfolio. Allocation of the portfolio is used to compute expected return of portfolio as it is weighted average of stock's return. =I, II, and III only

The common stock of Manchester & Moore is expected to earn 14 percent in a recession, 7 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 15 percent while the probability of a recession is 5 percent. What is the expected rate of return on this stock?

Probability of normal economy=(100-15-5)=80% Expected rate=Respective return*Respective Probability =(14*0.05)+(7*0.8)+(-4*0.15) which is equal to =5.7%

The expected return on HiLo stock is 14.70 percent while the expected return on the market is 13.6 percent. The beta of HiLo is 1.23. What is the risk-free rate of return?

Rf = Risk free rate Rm = expected return on the market = 13.6% Beta = Beta of the stock = 1.23 Required Rate of Return = 14.70% Calculation of risk free rate Required Rate of Return = Rf + (Rm - Rf) * Beta 14.70% = Rf + (13.60% - Rf) * 1.23 14.70% = Rf + 16.728% - 1.23 Rf 14.70% - 16.728% = RF - 1.23 Rf 2.028% = 0.23 Rf Rf = 2.028% ÷ 0.23 Rf = 8.81739% Rf = 8.82%

Which one of the following stocks is correctly priced if the risk-free rate of return is 4.5 percent and the market risk premium is 9.0 percent? Stock Beta Expected Return A .89 12.51% B 1.61 12.77 C 1.42 11.39 D 1.45 12.11 E .95 8.65

Risk free rate = 4.5% Market risk premium = 9% Stock A. Beta = .89 Expected return = 12.51% Required return = risk free rate + beta * market risk premium Required return = 4.5 + .89* 9= 12.51% Stock B. Beta = 1.61 Expected return = 12.77% Required return = 4.5+1.61*9= 18.99% Stock C. Beta = 1.42 Required return = 4.5+1.42*9= 17.28% Stock D Beta = 1.45 Expected return = 12.11% Required return = 4.5+ 1.45*9= 17.55% Stock E. Beta = .95 Expected return = 8.65% Required return = 4.5 + .95*9 =13.05% Stock is said to be correctly priced if required return is equal to expected return = Therefore stock A is correctly priced .

Consider the following information on three stocks: State of Probability Rate of Return if Economy of State of Economy State Occurs Stock A Stock B Stock C Boom .25 .27 .15 .11 Normal .65 .14 .11 .09 Bust .10 −.19 −.04 .05 A portfolio is invested 45 percent each in Stock A and Stock B and 10 percent in Stock C. What is the expected risk premium on the portfolio if the expected T-bill rate is 3.2 percent?

The expected return of stock A Expected return of stock A=(Expected return in boom ∗ Probability of boom)+(Expected return in normal ∗ Probability of normal)+(Expected return in recession ∗ Probability of recession) =(0.25×0.27)+(0.65×0.14)+(0.10×−0.19)= 0.1395 The expected return of stock B expected return of stock B= (0.25×0.15)+(0.65×0.11)+(0.10×−0.04)=0.105 The expected return of stock C Expected return of stock C=(0.25×0.11)+(0.65×0.09)+(0.10×0.05)= 0.09100 Now we will calculate the poftfolio return Poftfolio return= (Weightage of stock A ∗ Expected return of stock A)+ (Weightage of stock B ∗ Expected return of stock B)+ + (Weightage of stock C ∗ Expected return of stock C) = (45×0.1395)+(45×0.105)+(10×0.091)=11.91 The expected risk premium on the portfolio. expected risk premium =Poftfolio return − risk free rate= 11.91−3.2=8.71 = 8.71 %