Allocating Capital Across Strategies Using Returns and Sharpe Ratios
Summary
The document compares ways to allocate capital between two strategies when only their average daily P&L and Sharpe ratios are known. It infers daily volatility from those inputs, then distinguishes three objectives: maximize expected profit, minimize portfolio volatility, or maximize the Sharpe ratio. Each objective can produce a different allocation, so there is no single optimal split without knowing the investor’s goal.
For the stated example, the response recommends concentrating capital in the higher-return strategy to maximize profit. For minimum volatility, it gives a variance-based allocation; for maximum Sharpe under an assumption that returns are excess returns, it applies the Kelly-style return-to-variance rule. It also notes that correlation affects the preferred mix. The information is limited: correlation is not specified, and the alternative answer proposing weights directly proportional to P&L or Sharpe is not supported by a portfolio optimization argument. The resulting allocations therefore depend on assumptions and the chosen objective.
Key ideas
- Capital allocation depends on whether the objective is profit, low volatility, or a high Sharpe ratio.
- The stated daily P&L and Sharpe ratios imply different volatility levels for the two strategies.
- A minimum-volatility mix depends on the strategies’ variances.
- A Kelly-style maximum-Sharpe allocation scales each strategy by expected return relative to variance, under stated assumptions.
- Correlation matters to portfolio allocation, but it is not provided in the example.
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Full text
# How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?
# How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?
Let's say you have two trading strategies and all you're given is information about their average daily P&L and the Sharpe ratio of each strategy. Trading strategy A's daily average P&L is 10,000 USD and the Sharpe ratio is 5. Trading strategy B's daily average P&L is 5,000 USD and the Sharpe ratio is 10.
Given only this information (and nothing on correlation), how would you optimally allocate capital between the two trading strategies?
## Answer by Chris Taylor (score 9, accepted)
https://quant.stackexchange.com/a/35424
To be consistent with the average daily returns that you specified, your first strategy would need to have a daily standard deviation of 31,749 USD and the second a standard deviation of 7,937 USD.
How much weight you should assign to each strategy depends on your goal. You might want to maximize the daily profit, minimize the volatility, or maximize the information ratio. Each of these demands different allocations.
To maximize the daily profit, put all of your weight in the strategy with the highest expected return (strategy 1).
To minimize the volatility, you should weight each strategy according to the variance of the other strategy. This leads to putting 94.1% of the weight in the second strategy, and 5.9% in the first strategy. The exact ratio of the weights is 16:1, since the first strategy has 4x the volatility of the first (and hence 16x the variance).
To maximise the information ratio (equivalently the Sharpe ratio, assuming that the returns you mentioned are excess returns), the Kelly criterion then suggests that the allocation to each strategy should be proportional to the average return over the variance. Since the second strategy has half the expected return, and one-quarter the standard deviation, it should therefore receive 8x the capital allocation that the first strategy receives, since
$$ \frac{\frac{1}{2}}{\frac{1}{4}\times \frac{1}{4}} = 8 $$
If the strategies are somewhat positively correlated, you should allocated more to the second strategy (since it has higher Sharpe).
## Answer by WJA (score 0)
https://quant.stackexchange.com/a/35422
If you only have that type of information, then simply use:
```
w1 = 10000/(10000+5000)
w2 = 5000/(10000+5000)
```
Or replace the PNL by the Sharpe Ratio.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.