A simple PM question existing, another, simple, between, question

rohitdoshi

I have a portfoio worth $100,000. My existing portfolio's Sharpe Ratio is 0.12. I am thinking of taking another stock into my portfolio whose Sharpe Ratio is 0.10. I have calculated that the Correlation between my existing portfolio and the new stock is 0.3.

Can I take the new stock into my portfolio, if I do what will be the Sharpe Ratio of my new portfoio? Also, if I decide to take the new stock into my portfolio, what will be the optimal weightage ratio of that new stock and my existing portfoio so that the new Sharpe Ratio is maximum?

redskins44

I've studied this outside of this curriculum, and I don't think we are responsible for optimization. Right?

Anyway...

SHOULD you take in the new stock? The test is (current sharpe)*(correlation) = .12*.3 = .036. The new stocks sharpe of .10 is higher than .036, so, yes, you should consider adding the new stock.

What will be the new sharpe? Either there's some numerical gymnastic tricks that aren't coming to my mind, or you need to know the expected return of the current portfolio and the new stock, AND you need to know how much value you are adding.

At that point, you will have your weights, and will determined the combined expected values and combined portfolio variance (and std dev). New sharpe is (Rcomb - Rf)/STDcomb.

As for optimization, it's the highest point on the CAL. The slope of the CAL is the Sharpe ratio. The point of tangency will depend on the indifference curve, i think.

spreads

Can Add New asset to portfolio if:
New Asset Sharpe Ratio > Current Sharpe Ratio x Correlation of New Asset with Existing Portfolio

In this case:

0.1 > 0.12 x 0.3

So you will be able to add this asset to your portfolio.

Sorry, don't know about the second part, am at work and don't have my books with me.

Cheers,

Andrew