# Question - Pretty Simple. Explain answer.

1. A portfolio is equally invested in Stock A, with an expected return of 6%, and Stock B, with an expected return of 10%, and a risk-free asset with a return of 5%. The expected return on the portfolio is: A) 7.0%. B) 8.0%. C) 7.4%. 2) For the last four years, the returns for XYZ Corporation’s stock have been 10.4%, 8.1%, 3.2%, and 15.0%. The equivalent compound annual rate is: A) 9.2%. B) 9.1%. C) 8.9%.
1. Since the portfolio has equal weights, you compute the arithmetic average which is A) 7%. 2) Compounded annual return is calculated as a geometric average - therefore B) 9,1%.
1. E®p = Wa*E®a + Wb*E®b + Wc*E®c = .3333(.06) + .3333(.10) + .3333(.05) = 6.9999% = 7% 2) I don’t really understand what the question is asking here. If the returns given are all annualized (as one would assume) and he want an equivalent annual rate, then I guess we should just take the simple average of the four returns. ie. Avg (all four returns) = 9.175% = 9.2%

B for the first one. Equally invested in 6% and 10%, halfway point is 8. Or .33(6%)+.33(10%)+.33(5%) = 7% Second one you are looking for annualized geometric return, so add one, mulitply, take the nth root, subtract one 1.104*1.081*1.032*1.15 = 1.416^.25 = 1.0909 - 1 = 9.09 B Edit - sloppy reading on my part, I missed the risk free asset piece in the first q, corrected.

Mihau10…sorry for the dumb question but could you please explain how you got 9.1% using geometric average? I haven’t done geometric average yet…so I guess i might not be familiar! Thanks!

The answer is B for the first one. cmon guys: E[r] = w1R1 + w2R2 the weights are clearly 50% each. so… .5*6 + .5*10 = 8% The second one should be set up like this: (1.104*1.081*1.032*1.15)^(1/4) - 1 = 1.416^.25 - 1 = 9.092 = 9.1 Explanations: -Expected rate of return on a portfolio is simply the individual rates of return multiplied by their weight in the portfolio (adding up to 100%). in this case we have two, and they say that the shares are equal (50-50) so its just 50% of return of one plus 50% of return on the other. -The geometric mean tells us compound growth. it will always be less than the average but greater than the harmonic mean. Gmean = (1+R1*1+R2*…*1+Rn)^(1/n)-1

EMRA and Chi Paul you are forgetting that there was a w3r3 over there - with a 33% equal weighting on each of 6%, 10% and a Risk free asset of 5%. so your answer is 1/3 ( 6+10+5) = 7%.

Ha! This is true. i will edit my post. For some reason not seeing stock C made me ignore anything else afterwards. Thanks CP! -Emilio This is the real answer: > E = w1R1 + w2R2 + w3R3 > > the weights are clearly 33.3% each. > > so… > .333*6 + .333*10 + .333*5 + = 6.9%

Worst of all, I only corrected half of my post when I went to edit it. Idiot!

Nice guys…Thanks! I need to to stats soon…and understand the different means! Cheers…

mu and mean: population and sample, respectively. Done

CFA1 Buster Wrote: ------------------------------------------------------- > Mihau10…sorry for the dumb question but could > you please explain how you got 9.1% using > geometric average? I haven’t done geometric > average yet…so I guess i might not be > familiar! > > Thanks! Hi, I think EMRA32 has already explained the geometric average to you. Btw, no question is dumb - it’s better to ask and look for answers than don’t ask and don’t look for answers :).

Is there any simple and quick way to use HP 12C for calculation in the second question above (the geometric average one)? Thanks

graduate Wrote: ------------------------------------------------------- > Is there any simple and quick way to use HP 12C > for calculation in the second question above (the > geometric average one)? > > Thanks Dont let the notation discourage you. Have you seen the equation for arithmatic mean? its quite strange, yet so simple. Add them all together, divide by N. Its pretty much the same for geometric mean. Multiply them all together (add 1 if return is positive, subtract from 1 if return is negative) and use the [Y^x] key and punch in (1/n). That answer will be 1+r. so, just subtract 1 from it and voila! So… simple way is, multiply them all together, get the N root of your answer. subtract from 1. thats it. if you can do the arithmatic mean, you can do the geometric mean. The harmonic mean is more annoying, bunch of inverses divided by inverses. soo lame.