I have this not CFA specific urgent question about portfolio volatility neutralization. I would appreciate any ideas/thoughts/inputs.
Let’s say I have a portfolio that consists of 7 different stocks and GLD. I am asked to neutralize the volatility of the portfolio using SPX and RTY indexes (not futures). Also, I cannot use the indexes independently. I have to use both of them.
I have correlations, covariance matrix, variances of the portfolio and indexes. I am looking at correlations of the portfolio with both SPX and RTY and they are positive. So, I am assuming that I will have to short SPX and RTY in order to make the volatility neutral.
You will have to short at least one, but not necessarily both.
It will depend on the correlation of return between SPX and RTY, and will also depend on the standard deviations of returns of the portfolio, SPX, and RTY.
Because the correlation of returns of SPX and RTY is positive, you’re likely (though not necessarily) going to be long one, short the other.
Because the volatility of RTY is greater than that of SPX, you’re likely to be short RTY and long SPX.
(I ran it in Excel using Solver, telling it to minimize the standard deviation of returns of the combined portfolio. The solution was 86.7% original portfolio, 65.3% SPX, −52% RTY; the resulting portfolio has a standard deviation of returns of 14.28%.)
The result is somewhat similar to what you are getting and my approach is almost identical with yours. But the problem states that I should “neutralize the portfoilio volatility”, which I understood as making the combined portfolio’s standard deviation to be equal to 0.
Does “volatility neutralization” mean coming up with a hedging strategy that makes the total st.dev. equal to 0?
I would think that that’s what it means, but that isn’t possible unless you have a hedging vehicle whose correlation of returns with those of the original portfolio is −1.0.
So basically, you are saying: given a portfolio of 7 stocks + GLD, construct that portfolio using weights in SPX and RTY (and go short that replicating portfolio). This sounds impossible.
You can perhaps construct a zero Beta portfolio, but there are infinite solutions here.
When we talk about volatility of the portfolio, we are talking about the strandard deviations, right? But, would having a zero beta portfolio be considered as volatility neutralized portfolio?