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Does A Cash Balanced Portfolio Have A Higher Sharpe Ratio?

The stock market generates a better return than cash but is riksier than cash. One perfomance metric is the Shrpe ratio which measure the return per unit of risk. The unit of risk is the standard deviation of stock return. The following app helps us visualize how a cash balacnced portfolio affects the the investment portfolio.

Simulator

This app compares the investment results of a all SPY portfolio and a SPY/cash balanced one. Assume cash has both the return rate and return rate standard deviation are 0%.
Cash Ratio: %
SPY Ratio: %
SPY Mean Monthly Return: %
SPY Monthly Return Standard Deviation: %
Investment Duration: year(s).

Performance Comparison

Total Return

  • All SPY Portfolio: 0%
  • Cash Balanced Portfolio: 0%

Mean Return

  • All SPY Portfolio: 0%
  • Cash Balanced Portfolio: 0%

Return Standard Deviation

  • All SPY Portfolio: 0%
  • Cash Balanced Portfolio: 0%

Sharpe Rations

Result

The all SPY portfolio has a higher Sharpe ration in all circumsatance, which may result from the assumption that cash return is
The following Sharpe raion chart is accounts for cash return.
Cash Return: %

Conclusion

A pure market ETF portfolio such as SPY almost always has a better Sharpe ratio than a cash balances one, unless cash has some positive return. This makes sense because in reality short-term bonds yield can be seen as the cash return here, and can be used in the modeling app. This may be one of many reasons why with the Fed funds rate close to 0%, the stock mratket rises.
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