When a Negative-Return Asset Can Improve Portfolio Risk
Summary
This exchange considers whether an asset with negative expected return can still be useful when combined with a portfolio, especially if its returns are negatively correlated or uncorrelated with the portfolio. The answer focuses on expected return relative to volatility: without sufficiently negative correlation, adding the asset lowers the portfolio’s expected return and does not improve its expected return per unit of risk. At zero correlation, it adds dollar volatility, so the position must be offset by reducing exposure elsewhere or using leverage to restore the desired return.
The discussion distinguishes total expected return from return above the risk-free rate. A negative-return asset might be compatible with leverage if the risk-free rate is even lower, but the brief answer gives no sizing formula or worked example. Whether the asset helps therefore depends on correlation, expected returns, and the return benchmark used; the exchange does not establish a general rule for every portfolio or risk measure.
Key ideas
- An asset with negative expected return can reduce risk when its correlation with the portfolio is sufficiently negative.
- At zero correlation, the asset adds dollar volatility while lowering expected return.
- Leverage may restore a target return, but the answer gives no position-sizing method.
- The comparison changes when evaluating total return versus return above the risk-free rate.
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Full text
# Adding negative EV position to portfolio for diversification? # Adding negative EV position to portfolio for diversification? Say I have a portfolio of expected return $10\%$ and volatility $20\%$. If I have another asset that is either one of: - Negatively correlated - Positively correlated - Uncorrelated With negative expected return $\mu < 0$ and volatility $\sigma$. From intuition, I think that if we are allowed to use leverage, we should be adding this to portfolio under scenarios 1 and 3 to reduce risk (and apply leverage to achieve desire rate of return). Is this true? How would I size this position if I want to target $10\%$? Is this scenario similar to the case of shorting one asset and buying another that are positively correlated to each other? In both instances (long/short positively correlated or long/long negatively.. or zero correlated), they should be risk reducing. And if we're allowed to use leverage we should be ale to achieve target return at lower risk? Though this also depends on the bounds of expected return and correlation? Basically, is it ever smart to add something with negative expected value to a portfolio depending on its correlation to the portfolio? ## Answer by Mats Lind (score 1) https://quant.stackexchange.com/a/29778 If you're not in negative correlation territory you will not increase expected return over volatility with your negative return asset. Even at zero correlation it will add volatility (in dollar terms) but you need to decrease it to compensate for the decrease in return. Then again if you are talking about total expected return rather than the return minus the risk free rate, then a negative return would be fine in so far the risk free rate itself would be even lower (and you could use it to leverage your portfolio).
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