# Portfolio Theory: Must VarCovar Matrix be based on return var/covar?

I am trying to estimate the minimum variance portfolio where the assets are currency derivatives. In the specific case it does not make sense to base correlations or variance on asset returns. I am interested in getting a low variance in the actual value of the portfolio and not the returns. Can I just calculate the variance and correlation on the back of the individual asset value or does it have to be returns for the MVP theory to make sense?

It doesn't make sense to use the (co)variance(s) of asset values; if you did, by cutting an investment's share of the allocation by half, you would also cut its variance by a factor of 4. In a meaningful portfolio design, the volatility (variance) of an asset, by itself, is the same no matter how much or how little of your portfolio you put in it.

Why doesn't it make sense to use correlations and variance of RETURNS for currency derivatives?

• Okay I see. What I would like to have is a portfolio of currency derivatives where the actual value of the portfolio is as stable as possible. The traditional minimum variance portfolio is constructed so that the return on the portfolio is as stable as possible. What I would like is for the return over time to be as close to zero as possible. Apr 24, 2016 at 8:19
• You probably didn't mean what you said - you may want to clarify. If you want a return as close to zero as possible, all you need to do is to keep your money under the mattress, you don't need a portfolio of currency derivatives to achieve that goal. Or if you must invest in derivatives, you can buy USD/Euro and Euro/USD futures contracts in the same amounts (but you will be out the commissions).
– user20429
Apr 24, 2016 at 12:06
• My question was just to address a "small" issue in a way more complicated setup but I think that I have found a solution to my problem. Thank you very much for your time anyway! Apr 24, 2016 at 13:43

You need to model the underlyings, price the derivatives, and then measure risk.

• That is true - and disconnected from the question the OP asked.
– user20429
Apr 24, 2016 at 12:07
• Oh. I don't really get what his question is then. Apr 25, 2016 at 15:41
• Normally you use the standard deviations and correlations of total returns in developing efficient portfolios. He wanted to know if instead of "returns" you can use standard deviations and correlations of "dollar amounts" invested in each vehicle to do the same mean-variance tradeoff computations.
– user20429
Apr 25, 2016 at 15:53
• Cool, glad you cleared it up for him. Apr 25, 2016 at 16:16