Sharpe Ratio is Different when Position Size % is Different

riskfreealpha

The Sharpe ratio is supposed to be the same regardless of how much cash % is in the portfolio (ex: 90% vs 5%). However, I am getting two different sharpe ratios for the same strategy but with a different cash position. Here is the code:

class MaCrossStrategy(bt.Strategy):

    def __init__(self):
        pass
        ma_fast = bt.ind.SMA(period= 50)
        ma_slow = bt.ind.SMA(period = 200)

        self.crossover = bt.ind.CrossOver(ma_fast, ma_slow)

    def next(self):
        if not self.position:
            if self.crossover > 0:
                self.buy()
        elif self.crossover < 0:
            self.close()


cerebro = bt.Cerebro()

data = bt.feeds.YahooFinanceData(
        dataname = 'SPY',
        fromdate = datetime.datetime(2000, 1, 1),
        todate = datetime.datetime(2021, 4, 4)
)
cerebro.adddata(data)
cerebro.addstrategy(MaCrossStrategy)
cerebro.broker.setcash(1000000)
cerebro.addsizer(bt.sizers.PercentSizer, percents = 10)
cerebro.addanalyzer(btanalyzers.SharpeRatio, _name = "sharpe")
cerebro.addanalyzer(btanalyzers.Transactions, _name = "trans")
cerebro.addanalyzer(btanalyzers.TradeAnalyzer, _name = "trades")
back = cerebro.run()
print('Ending portfolio value: {:,.0f}'.format(cerebro.broker.getvalue()))
print(back[0].analyzers.sharpe.get_analysis())
print(back[0].analyzers.trans.get_analysis())
profit = cerebro.broker.getvalue() - 1000000
print('total profit: {:,.0f}'.format(profit))
cerebro.plot()

The Sharpe ratio I get for sizer = 10 (cerebro.addsizer(bt.sizers.PercentSizer, percents = 10) is -0.212 but the Sharpe ratio I get for sizer = 95 is 0.67.

What is the reason for this and how can I solve it?

run-out

@riskfreealpha said in Sharpe Ratio is Different when Position Size % is Different:

The Sharpe ratio is supposed to be the same regardless of how much cash % is in the portfolio (ex: 90% vs 5%).

What do you base this assumption on?

riskfreealpha

@run-out if you start out with a portfolio with no cash and then increase it to 50% cash, the expected return and standard deviation are also halved, thereby leaving the Sharpe ratio unchanged.