Seems to me that if you can not rely on standard deviation to give you a risk-adjusted profile due to the asymmetrical returns of Alt investments (say hedge funds that invest in options), than how can you write in an answer that Alt investments have good diversification benefits due to low correlations with other asset classes…

but doesn’t the calculation for correlation use standard deviation?

Sorry if this is not sometime that would probably be “directly” tested, but just curious.

the first statement relates to the use of sharpe ratio for a portfolio with options embedded in them - bcos with the options your returns are inflated - and your std deviation is reduced. as a result sharpe ratio will be inflated.

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use of correlation to detemine correlation is ok - possibly because you are not making a one - asset determination like the above case. there is a interplay of correlations for diversification purposes. (both numerator and denominator for diversification have correlations) - and they will move up or down together … not numerator becoming bigger and denominator becoming smaller - for the alt investments hedge funds with options case…

This is a good point as the pearson correlation coefficient requires bivariate normality in order to completely describe the relationship between the two variables, but it doesn’t require normality for use. In short, the pearson correlation coefficient won’t give you as good of an idea about the relationship if even one of the variables is not univariate normal.

Just as an aside: univariate normality is required in both variables in order to have the possibility of bivariate normality (in general, univate normality is required in all variables for the possibility of multivariate normality). However, each being univariate normal does not guarantee the multivariate normality.

I see your point in terms of how the std deviation is reduced with inflated Sharpe ratios. I think what I was trying to say is, if we know that the st deviation does not capture the total risk or “true” volatility due to asymmetrical returns, then wouldn’t it be fair to say that the st deviation metric is not a metric that can be used in these types of vehicles…

If so…

Then how can I conclude that hedge funds can give diversification benefits by looking at the correlations, given that correlation in itself uses standard deviation to calculate, which what I think we are both agreeing that it is not a reliabile statistic given the asymmetrical returns.

I guess I can apply the same logic to bonds…

I know that I can not be correct here, there has to be some answer on the reason why, I just can’t figure it out.

While this is true, you’re overlooking the fact that the pearson correlation coefficient doesn’t require normality for describing an association between variables. Remember what it’s doing: it’s measuring a linear relationship. It is possible, that despite having non-normally distributed returns, the relationship between the two return series is linear (and the pearson correlation is presumably accurate). However, without bivariate normality, it’s also possible that the correlation coefficient isn’t capturing the full relationship of the variables (the returns, in this case, might have a non-linear relationship).

If you’re concerned about the pearson correlation not adequately representing the correlation of the returns between a hedge fund and the market, you could always plot the returns in a 2-dimensional space and examine the plotted relationship. If it appears linear, then the pearson correlation coefficient is probably doing an okay job at describing the relationship (and giving you some insight into diversification benefits). If it’s non-linear, you can see for yourself the nature of the association (one approach).

Also, remember your basics. A normal distribution is adequately described by the mean and variance/standard devation. So, a sharpe ratio, or similar metric, needs that normality for the interpretation to be accurate. Without normality, you need more parameters to describe the distribution accurately.