Inv Managment exam 2

XYZ stock price and dividend history are as follows: 2010 Beginning of year price: 100, divdend paid: 4 2011 Beginning of year price: 110, divdend paid: 4 2012 Beginning of year price: 90, divdend paid: 4 2013 Beginning of year price: 95, divdend paid: 4 An investor buys three shares of XYZ at the beginning of 2010, buys another two shares at the beginning of 2011, sells one share at the beginning of 2012, and sells all four remaining shares at the beginning of 2013. (LO 5-1) a. What are the arithmetic and geometric average time-weighted rates of return for the investor? b. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2010, to January 1, 2013. If your calculator cannot calculate

2011: rate of return=((110-100+4)/100)*100=14% 2012: rate of return=((90-1104/100)*110=-14.55% 2013: rate of return=((95-90+4)/100)*90=10% Arithematic mean: =(14%-14.55%+10%)/3=3.15% geometric mean=[(1+.14)*(1-.1455)*(1+.1)]^(1/3)-1=2.33% Dollar weighted return=300=(-208/IRR)+(110/IRR)^2+(396/IRR)^3=-.1661%

The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Boom: Divdend $2 and stock price of $50 Normal Economy: divdend of $1 and stock price of 43 Recession: divdend of.5 and stock price of 34 a. Calculate the expected holding-period return and standard deviation of the holdingperiod return. All three scenarios are equally likely. b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%.

Boom Case: HPR=(50-40+2)/40=.3 Normal Case: HPR=(43-40+1/40)=.1 Recession Case: HPR=(34-40+.5)/40=-.1375 Expected returns=(1/3*.3)+(1/3*.1)+(1/3*(-.1375))=8.75% Var=[(1/3(30-8.75)^2]+[(1/3(10-8.75)^2]+[(1/3(-13.75-8.75)^2]=319.79 St.dev=sqrt(319.79)=17.88% B. E(rp)=.5*8.75%+.5*4%=6.375% St.dev=.5*17.88%=8.94%

Using the historical risk premiums as your guide, what is your estimate of the expected annual HPR on the S&P 500 stock portfolio if the current risk-free interest rate is 5%?

E(rp)=rf+(rm-rf) =5%+8.34%=13.34%

You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client's portfolio?

Expected return on equity is 16% (.6*.16)+(.4*.06)=12% which is expected return on clients portfolio standard dev=(.14*.6)=8.4%

What do you think would happen to the expected return on stocks if investors perceived an increase in the volatility of stocks?

If an investor perceived an increase in volatility of stocks then he will expect more return on stocks to comepsate for risk.

Suppose your expectations regarding the stock market are as follows: Boom: Probabily is .3 and HPR is 44% Normal Growh: Prob is .4 and HPR is 14% Recession: Prob is .3 and HPR is -16% Use Equations 5.10-5.12 to compute the mean and standard deviation of the HPR on stocks.

Mean distribution of HPR on stocks=(.3*44)+(.4*14)+(.3*(-16))=14%

To estimate the Sharpe ratio of a portfolio from a history of asset returns, we use the difference between the simple (arithmetic) average rate of return and the T-bill rate. Why not use the geometric average?

Sharpe ratio also known as the reward to volatility ratio tells how much a investor is getting from a portfolio per unit of the risk taken by him/her. It is used for ranking different portfolios the basis of risk-return trade off S=Portfolio Risk Premium/Standard dev of portfolio excess return= (E(rp)-rf)/op Hence portfolio risk premium =E(rp)-rf In the Sharpe ratio, the expected rate of return on portfolio is calculated based on arithmetic average. While geometric average is more useful in cases of series where events are dependent, arithmetic average proves better in cases of series where events are independent. In case of different portfolios, returns will be independent of each other. Additionally geometric average incorporates compounding which can overstate the results of the Sharpe ratio

When estimating a Sharpe ratio, would it make sense to use the average excess real return that accounts for inflation?

When the estimate for the Sharpe Ratio measure is done, if the average excess real return that accounts for inflation is used then the ratio calculated will not be appropriate because all items in this measure are calculated using nominal figures, so the inputs should also be nominal as well

You've just decided upon your capital allocation for the next year, when you realize that you've underestimated both the expected return and the standard deviation of your risky portfolio by 4%. Will you increase, decrease, or leave unchanged your allocation to riskfree T-bills?

The primary objective of capital allocation is to diversify risk involved investing through money in different classes. Since expected returns and Standard dev of risky portfolio is estimated to increase by 4%, it means the return to volatility ratio of the portfolio will decrease overall. This is due to the fact that increase in each unit of standard dev will be more than increase in each unit of return. To make overall return increased to its original level, allocation to risk free T Bills needs to be decreased so more returns can be expected from risky portfolio

The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.5 and a residual standard deviation of 30%. (LO 6-5) a. What would make for a larger increase in the stock's variance: an increase of .15 in its beta or an increase of 3% (from 30% to 33%) in its residual standard deviation? b. An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in stock A. Which of the changes in (a) will have a greater impact on the portfolio's standard deviation?

a. ((1.65^2*.2^2))+.3^2=.1989 (1.5^2*.2^2)+.33^2=.1989 b. In both cases the stock variance will increase from .18 to .1989

Suppose the same client in the previous problem decides to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. (LO 5-3) a. What is the proportion y? b. What are your client's investment proportions in your three stocks and the T-bill fund? c. What is the standard deviation of the rate of return on your client's portfolio?

a. .08/.1=.8 b. .8*.27=.2160 .8*.33=.2640 .8*.4=.32 c. .8*.27=.2160

A portfolio's expected return is 12%, its standard deviation is 20%, and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio's Sharpe ratio? (LO 6-3) a. An increase of 1% in expected return. b. A decrease of 1% in the risk-free rate. c. A decrease of 1% in its standard deviation.

a. .13-.04/.2=.45 b. .12-.03/.2=.45 c. .12-.04/.19=.42 part a and part b

14. Suppose the same client as in the previous problem prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%. (LO 5-3) a. What is the investment proportion, y? b. What is the expected rate of return on the overall portfolio?

a. 2./.27=.7407 b. E(rc)-.07=.7407*(.17-.07)=.14407

a. Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in Equation 5.17 is A = 4, what would be a reasonable guess for the expected market risk premium? b. What value of A is consistent with a risk premium of 9%? What will happen to the risk premium if investors become more risk tolerant?

a. E(r)-rf=Ao^2=4*(.2)^2=16% b. .09=A*.2^2 A=.09/.2^2=2.25 c. An increase in risk tolerance level of an investor means his risk aversion(A) will decrease as he will now be less reluctant to take the risk. As a result, he will deman less risk premium

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of .5. The alternative riskless investment in T-bills pays 5%. (LO 5-3) a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now? d. Comparing your answers to (a) and (c), what do you conclude about the relationship between the

a. Expected cash from portfolio=CFs1*p(s1)+CFs2*p(s2)=(50000*.5)+(150000*.5)=100000 required rate of return is 15% amount of investmetn=100000/1.15=86956 b. expected cash flow=100000-86956/86956=15% c. required rate of return is now 20%, amount needed to invest=100000/1.2=83333 d. price of investment will decrease with increase in risk premium and vice versa

For Problems 12-16, assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. 12. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. (LO 5-3) a. What is the expected return and standard deviation of your client's portfolio? b. Suppose your risky portfolio includes the following investments in the given proportions: Stock A 27% Stock B 33% Stock C 40% c. What is the Sharpe ratio (S) of your risky portfolio and your client's overall portfolio? .d. Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund's CAL.

a. Expected return=.7*17%+.3*7%=14% stand dev=.7*27%=18.9% b. proportion of stock A=.7*.27=.189 proportion of stock B=.7*.33=.231 proportiono f Stock C=.7*.4=.28 c. .17-.07/.27=.3704 of overall portfolio=.14-.07/.189=.3704 d.

You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 13% with a standard deviation of 25%. Draw the CML and your fund's CAL on an expected return/standard deviation diagram. (LO 5-4) a. What is the slope of the CML? b. Characterize in one short paragraph the advantage of your fund over the passive fund.

a. slope of cml=.13-.07/.25=.24 slope of cal=.17-.07/.27=.3704 b. since the investor's fund has a higher slope than of the passively managed fund an investor can expected a higher rate of return

When adding a risky asset to a portfolio of many risky assets, which property of the asset is more important, its standard deviation or its covariance with the other assets? Explain.

an investor will be more concerned about covariannce due to reaping the benefits of diversification