Hello all,
I have a question on why having a zero beta is fruitful.
In my mathematical statistics class my professor kept hammering down that covariance is the linear dependence of the two variables.
My question is: how do we calculate non-linear dependence between two 'random variables' ,'stocks', so on?
Kristen,
Having a low beta is one indication that the strategy you have picked is unique and perhaps repeatable without disruption by market forces, a money printing algo that won't be destroyed by a market meltdown.
A beta of one, meaning that you are tracking the broad market, means that your strategy is subject to all the factors that move the market: interest rates, monetary policy, political environment, economic growth, inflation, etc... All items that are highly unstable and thus result in unknown future performance. Also, if you have a strategy with a beta of one, you are likely better investing in a low-cost index fund, than executing your algo.
A beta of zero is one indicator that you have found a strategy that will produce returns regardless of the vagaries of the market. You have found some anomaly that will produce positive returns consistently regardless of market conditions.
It is only one indicator though, you can easily construct a zero beta strategy that would be a disaster. If you sold out of the money puts, you would have a high return, low beta, high sharpe ratio strategy, until the market crashes and you lose all your money.
As for other methods to assess dependence, Quantopian has Spearman rank correlations available, which helps to see if the data is monotonic. It can help you assess non-linear dependencies better than Pearson.
Hope that helps. Keep studying and hammer your professor back.
Best
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