Betsy Minor is considering the diversification benefits of a two stock portfolio. The expected return of stock A is 14 percent with a standard deviation of 18 percent and the expected return of stock B is 18 percent with a standard deviation of 24 percent. Minor intends to invest 40 percent of her money in stock A, and 60 percent in stock B. The correlation coefficient between the two stocks is 0.6. What is the variance and standard deviation of the two stock portfolio? A) Variance = 0.02206; Standard Deviation = 14.85%. B) Variance = 0.04666; Standard Deviation = 21.60%. C) Variance = 0.03836; Standard Deviation = 19.59% Apparently, we have to know the calculation for the stdev of a portfolio consisting of 2 risky assets i and j: w = weight s=stdev (si^2)*(wi^2)+(sj^2)(wj^2)+2*wiwjsisjCorrij
It is so easy to make a mistake using that formula. One wrong decimal place and it’s all wrong.
^ yep.
Me knowing that for the exam = highly unlikely.
It looks a lot more intimidating than it really is. It’s just a pain in the ass to plug and chug. There’s a formula for variance of a 3 asset portfolio.
I think in most of these questions we dont need to calculate anything. There is a similar question (which is much bigger). The answer without doing the calculation should be A. My trick is to multiply the weights with the corresponding standard deviations. (0.4*14)+(0.6*18)=16.4% (this is the standard deviation if the assets were perfectly positively correlated r=+1) since in this case the correlated=+0.6
i faithfully used the formula and the answer is C.
kh.asif Wrote: ------------------------------------------------------- > I think in most of these questions we dont need to > calculate anything. There is a similar question > (which is much bigger). > > The answer without doing the calculation should be > A. My trick is to multiply the weights with the > corresponding standard deviations. > > (0.4*14)+(0.6*18)=16.4% (this is the standard > deviation if the assets were perfectly positively > correlated r=+1) > > since in this case the correlated=+0.6 would be diversification benefits and portfolio > risk would be less than 16.4%. don’t do that on the exam. i take C as well. one mark lost for about 30 seconds more work.
kh.asif Wrote: ------------------------------------------------------- > I think in most of these questions we dont need to > calculate anything. There is a similar question > (which is much bigger). > > The answer without doing the calculation should be > A. My trick is to multiply the weights with the > corresponding standard deviations. > > (0.4*14)+(0.6*18)=16.4% (this is the standard > deviation if the assets were perfectly positively > correlated r=+1) > > since in this case the correlated=+0.6 would be diversification benefits and portfolio > risk would be less than 16.4%. So you’re saying that since the correlation is less than 1, the portfolio standard deviation must be less than the weighted average of 16.4%, so you think the answer is A?
CFAtime Wrote: ------------------------------------------------------- > kh.asif Wrote: > -------------------------------------------------- > ----- > > I think in most of these questions we dont need > to > > calculate anything. There is a similar question > > (which is much bigger). > > > > The answer without doing the calculation should > be > > A. My trick is to multiply the weights with the > > corresponding standard deviations. > > > > (0.4*14)+(0.6*18)=16.4% (this is the standard > > deviation if the assets were perfectly > positively > > correlated r=+1) > > > > since in this case the correlated=+0.6 there > > would be diversification benefits and portfolio > > risk would be less than 16.4%. > > > So you’re saying that since the correlation is > less than 1, the portfolio standard deviation must > be less than the weighted average of 16.4%, so you > think the answer is A? I am really sorry. While I think my crude method is not incorrect, I applied the wrong standard deviations. I did —>(0.4*14)+(0.6*18)=16.4% It should be—>(0.4 *18)+(0.6*24)=21.6% (This would be answer if the correlation was +1). However with correlation<1, the standard deviation has to be<21.6%. In any case, it is best to do the whole calculation which as nicob stated would not take much time. Sorry for the messup.