# Portfolio Management

I didn’t find this funny, at this point in time… Reed N. Wright, CFA, compiled the following information about the returns of the common shares of the Ajax Gidget Corporation: Range of Returns ******* Percentage of Years Returns within Range -10 up to 0%********20 0 up to 10********50 10 up to 20********30 Reed is thinking of constructing a portfolio with 40% of assets in Ajax Gidget shares and the rest in a one-year Treasury bill that can be purchased to yield 4%. Reed asks you, as an Analyst Forum Experts, what the expected return and standard deviation of such a portfolio should be? You’re best answer should be: a. The expected return of the portfolio will be 5.2% and the standard deviation of the return will be 2.8%. b. The expected return of the portfolio will equal the weighted average of the expected returns of the risky and risk-free assets. Furthermore, the standard deviation of the possible portfolio returns will also equal the weighted average of the standard deviations of the risky and risk-free assets. c. The expected return of such a portfolio will equal the weighted average of the expected returns on Ajax shares and the risk-free return. Furthermore, the standard deviation of the possible portfolio returns will be 7.0%. d. The expected return of the portfolio will be 4.8% and the standard deviation of the return will be 2.16%. - Dinesh S

B? By breaking up the 3 bins of Ajax and choosing the midpoints of the three bins, I find Ajax to have mean return =6%. Additionally =85, implying StdDev = sqrt(-^2)=7%. Choosing the porfolio if 0.4 Ajax + 0.6 * T-Bill, I calculate a weighted portfolio expected return of 4.8% with a StdDev of 2.8%. Since none of the other three answers agree with these numbers I choose B.

Dinesh, where did you find this question? I believe the ER = .06, and the STD = 5.9, which isn’t one of the choices…what is the answer?

B Er(ajax) = 6%, Std Dev. = 2.8% Risk free rate has got no standar deviation (0), so the portfoio’s std. dev is simply the weighted ave.

ok, i’m wrong, but I redid my numbers. The ER of the portfolio is 4.8%. How can you figure out the cost of the debt if you do not know the tax rate?

I apologize for being retarded but can somebody post their STD calculations something doesnt work out for me

Sorry I got it now too late… or should I say too early?

I’ll go with B as well

someone… I am losing my mind over this. Xi # of obs. Prod -5 20 -100 5 50 250 15 30 450 Mean = 6 For Std Dev : Aren’t we supposed to do Sum (Xi-Xbar)^2/n and take sqrt of that? and I get sum((xi-xbar)^2 ) = 203. so my stddev = sqrt(2.03) = 1.4247

cpk you have to take into account the weights as well, calculate the the std and then multiply by 0.16 for the portfolio one

that is for the portfolio… that I understand. Figure of 1.42… itself I am just checking with you to see if that is correct as StdDev for Ajax gidget. Yes, Portfolio stddev = 0.4 * 1.4247 = .5699

mine equals to 2.8% 11^2*0.2+1^2*0.5+9^2*0.3=49 std stock =7 - portfolio 7*0.4=2.8 am I wrong?

ok… thanks for clarifying that… I was missing the frequency multiplication part… and doing it as though these were separate numbers…

yeh i reckon answer is B aswell… avg is 4.8… st dev is 2.8…

Please you guys are on the roll… The correct answer is B. I did a shortcut here (and got it wrong). I simply calculated the expected return of the portfolio to be 4.8% and chose D. Mulit-part problems kinda are time consuming - Dinesh S

Dinesh, Just an idea that you do not have to calculate everything to the end - let: w1 = w(riskfree) r1= return on riskfree s1=sigma(riskfree) w2 = w(asset) r2= return on asset s2= sigma(asset) #1. E(port) = w(1)*r(1) + (1-w(1))*r(2) thus linear function! #2. sigma(port) = sqrt [w1^2*s1^2+(1-w1)^2*s2^2+2w1w2s1s2*rho] the trick here is to recognize that: s1=0 because there is no variation in the return. thus: sigma(port) = sqrt [(1-w1)^2*s2^2] sigma(port) = (1-w1) *s2 this is linear too. so no computation needed - just remember: both return & risk are linear functions when combined with risk-free assets. q.e.d

Yup, this question is more to test your understanding that the variance of the risk free rate is zero the covariance of any portfolio with the risk-free asset is zero