If correlation of new asset with existing portfolio is -1, do you add it or not, using Sharpe ratio analysis. Also, can you have a negative Sharpe ratio…what would it mean?
If the correlation is -1 you are definitely going to add it as long as the Sharpe ratio of the portfolio is positive. It is possible to have a negative Sharpe ratio, which means the portfolio is destroying value and you are better off just placing your fund in the risk free asset.
I can positively assure you that there are traders out there that have negative Sharpe ratios that last for years. Go figure. If r = -1 and the expected return is positive then you should always add it. If the expected return is negative it’s not clear and depends on the expected returns of the rest of the portfolio and the variances. Realistically an r of -1 means you just have the opposite of your portfolio now, e.g., you own S&P 500 and the new asset is a deep ITM put which wouldn’t help your portfolio
If Rf=5% and my current portfolio’s E(Rp)=10% with STDp=20%. So, current Sharpe_p = 0.25 (for every 1% added risk, I get 0.25 extra return). If another asset has correlation=-1 with my portfolio, and it has E(Ra)=12%, and STDa=25%. My portfolio’s Sharpe is positive. If I add this new asset, and it gets the expected 12% return, my portfolio’s return without the asset will be negative (they are negatively correlated), so how do I gain by adding the new asset? I’m now starting to review PM and concepts like these are blurred in my mind.
-1 correlation basically means that you have the exact opposite of something else in your portfolio, which would include any alpha effect. So, you might want to add this asset to your portfolio to reduce risk.
ohai Wrote: ------------------------------------------------------- > -1 correlation basically means that you have the > exact opposite of something else in your > portfolio, which would include any alpha effect. > So, you might want to add this asset to your > portfolio to reduce risk. If the objective is to reduce risk without regards to return, then buy Rf.
You might not want to sell risky assets to reduce risk due to liquidity constraints.
Dreary Wrote: ------------------------------------------------------- > If Rf=5% and my current portfolio’s E(Rp)=10% with > STDp=20%. So, current Sharpe_p = 0.25 (for every > 1% added risk, I get 0.25 extra return). If > another asset has correlation=-1 with my > portfolio, and it has E(Ra)=12%, and STDa=25%. > > My portfolio’s Sharpe is positive. If I add this > new asset, and it gets the expected 12% return, my > portfolio’s return without the asset will be > negative (they are negatively correlated), so how > do I gain by adding the new asset? > > I’m now starting to review PM and concepts like > these are blurred in my mind. You need to work out the portfolio std dev which depends on the weights (you have the formula in your book). The basic gist is that negative correlations reduce the portfolio variability. In this case since r = -1 you can get a portfolio that has zero variability. If the expected return > 0 this gives an infinite Sharpe ratio.
You add the asset to portfolio if, Portfolio with asset Sharpe ratio > Portfolio without asset Sharpe ratio * correlation of asset with portfolio. Most of the case, adding asset with -ve correlation reduces risk.