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Stock Picking

chrisjones

Joined
2/16/12
Messages
3
Points
11
|Stock| Expected Return| Volatility|
|A | 10% | 10% |
|B | 15% | 20% |

You have 1m to invest in either A,B or a combination. Assume stocks are completely independent of each other.

1. How can you maximise your return?
2. How can you minimize volatilty.
3. How can you maximise the sharp ratio of a portfolio

I was going for a programming role and got asked this, I answered
1. 1m B
2. 1m A
3. you will find the max of the portfolio if you find the derivitie of the sharp ratio and equate to 0??
 
That looks about right. You just need to know the formula for E[R] and Variance of the 2 assets with weights.
 
Thanks passyingby, can you be a bit more specific. I have never really worked in front office so no idea how to calculate #3.
 
Take a look at http://en.wikipedia.org/wiki/Modern_portfolio_theory.

E(R) is just weight A * return A + weight B * return B
Var = weight A^2 * stdev A^2 + weight B^2 * stdev B^2 + (Something that gets multiplied by the correlation. This becomes 0)

So you're trying to maximize E(R) / Sqrt(Var) -> which you can do by taking the derivative and setting to 0. weight B = 1-weight A.

This isn't really a front-office thing. Trust me traders aren't doing this.
 
The Sharpe ratio depends on the risk-free rate of return. The stocks are independent, so their variances are linear. A portfolio with 1 unit of each stock will have a variance of 1/2 * (0.1^2 + 0.2^2) = 0.025, or a volatility of sqr(0.025) = 15.81%. It would also have an expected return of 1/2 * (10% + 15%) = 12.5%. If the risk-free rate is 0%, and we call the 50% A/50% B portfolio P, then A has the best Sharpe ratio, then P, then B. But what if the risk-free rate is 9%? Now B has a Sharpe ratio of 0.3, P has a Sharpe ratio of 0.22, and A has a Sharpe ratio of 0.1.

Maybe my calculus is subpar, but I can't think of a way that allows you to deterministically say which portfolio has the best Sharpe ratio without knowing ahead of time what the risk-free rate of return is. Of course, if you wanted to use partial derivatives you could simply provide a set of solutions with the risk-free rate as a parameter.
 
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