for part B in hw, I was trying to following the formula. Can someone tell me where i did wrong?

Vp = (x1)^2 * V1 + (x2)^2 * V2+ (x3)^2 * V3+ 2*x1*x2*Cov(1,2) + 2*x1*x3*Cov(1,3) + 2*x2*x3*Cov(2,3)

Vp = (0.5)^2 * 0.2^2 + (0.3)^2* 0.3^2 + (0.2)^2 *0.4^2+ 2*0.5*0.3*0.5 + 2*0.5*0.2*0.3 + 2*0.3*0.2*0.1=0.2465

Got the same answers, thanks for checking!

There is a Quiz Question in the textbook designed specifically for a 3-stock portfolio.  In the sixth edition it is problem #8.  It shows you the nine boxes you need to sum.

I also got the same answers for both variance and SD of the portfolio.

i agree with the .03974 and .19935.

The variance formula is easily extended to multiple variables if you use a little matrix algebra. Say SD is an nX1 standard deviation vector, SD' is the transpose and P is the nXn correlation matrix. Just multiply SD' X P X SD (in this case, you'll want the weights multiplied to the corresponding entries in the SD vectors before you start).

There was a fair bit of arithmetic on this homework so I just want to check with people to see if our answers line up for (B) and (C).

For (B) I got that the variance of portfolio is 397.4 (or .03974 if you use decimals instead of %'s)

for (C) I got a standard deviation of 19.934894% (or .19934894). Anyone else get those answers?

 

Quick one for NEAS:

Why are the Standard Deviations %ages? 

I ended up using .20 (for example) rather than 20, and got a very, very small variance.  Is that going to be acceptable, or should I be using 20 and the % sign is just an error or something?

[NEAS: The standard deviations are percentage points.  For Stock A, the expected return is 10% per annum.  A return 2 standard deviations above the mean is 50% per annum.  A return 2 standard deviations below the mean is -30% per annum.]

Jacob: How do we determine the correlation between the returns on two stocks? In this homework assignment, we are given the correlations. In practice, how do we derive them?

Rachel: The correlation ρ_a,b is defined as the covariance between the returns on stocks A and B divided by the product of the standard deviations of stocks A and B:

ρ_a,b = covariance(A,B) / (σ_a × σ_b)

If we have a sample of returns, such as returns for the 252 trading days in the year, the correlation is

Jacob: Do we use this formula to derive correlations between stocks?

Rachel: The high stochasticity of stock returns causes random fluctuations to overwhelm the true correlation. Many analysts assume the same correlation exists between any two firms in an industry. We examine the correlations of several large stock insurers, take the average, and assume the average holds for all insurers.

Jacob: The correlation between two auto insurers is greater than that between an auto insurer and a life insurer.

Rachel: We use averages of insurers of the same type. But much of the correlation estimate is judgment; we don’t always have good data.