Alternative Investments -Measuring Performance

How to measure performance between accounts.

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Dealing in Alternative Investments requires a bit of statistical knowledge (the more the better).  So I picked out one component that would benefit someone who handles their investments personally and, at the same time, benefit someone who pays an advisor because it never hurts to ask the right questions.

The following is not investment advice, but one way to assess the advice you were given…

High Frequency Trading or Unconventional Return Periods

When returns are realized at higher frequencies (many times per year), Sharpe Ratios and the corresponding t-statistics can be calculated in a straightforward way.

Assuming there are N return occurrences per year, and the mean (μ) and standard deviation (σ) of the returns are μ and σ, the annualized Sharpe Ratio can be calculated as (μ×N)/(σ×√N) …or (μ/σ)×√N.

The corresponding t-statistic is (μ/σ)×√(N × number of years).

For monthly returns, the annualized Sharpe Ratio and the corresponding t-statistic are (μ/σ)×√12 and (μ/σ)×√(12 × number of years), respectively.  Here, μ and σ are the monthly mean and standard deviation of returns.

Similarly, assuming μ and σ are the daily mean and standard deviation for returns (you traded every day the market was open…please don’t do that:) and there are 252 trading days in a year, the annualized Sharpe Ratio is (μ/σ)×√252 …the corresponding t-stat is (μ/σ)×√(252 × number of years).

The calculators I use to find these metrics are listed in the right-hand column on “my trading desk.” They both have statistical functions.

The Test Statistic

Test Statistics (t-stat,t-statistic) are tricky creatures.  Essentially when evaluating performance, I require a t-stat of 4 or more (the higher the better) before considering a stake.  In the future, I will explain a simple model I use to allocate cash among accounts and strategies according to their t-stat.

Now, here is a simple formula to estimate a t-statistic for unusual return periods:

Test statistic= (μ/σ)×√(N return occurrences × number of years).

Note that “N return occurrences×Number of years” is just the total number of return occurrences resulting from the investment or strategy (either positive or negative).  So, if you closed out 3 trades (at 1%, -2.3% and 3%), that counts as N=3.

Or, if an investment reconciled every 6 weeks, for the past 1.5 years then N=13, (78 weeks / 6).

Remember, it is important to convert your daily/weekly/monthly returns to an annual (yearly) number.  This makes it very easy to compare performance against conventional, low-return investments pushed by financial salesmen.

And since the volatility adjustment is built-in, it is an apples-to-apples comparison.

 

Author: Alexander Zhang's Blog

The ocean is my home, although I don't miss living on a ship! Risk Manager & Author from San Francisco.