### The power of Cash position, Part 2: A toy model with known probabilities.

A brief addendum to the Part 1.

**Can the volatility drag quantified by the simulation that was performed in the previous post?**

Let’s construct the toy SPY model in a way that the** Expected %change is a positive constant every day, but very, very close to zero. (For example = 0.00001)**

A naive observer would say that in this case, the Buy & Hold strategy would be profitable, since every day has a positive expected outcome, so it is worth taking a Long position in equities.

That is not the case.

And we show here that the outcome largely depends on the SD.

**Assuming Gaussian distribution, the real world SPY has a mean 0.000384, that is 0.0384% and a Standard Deviation (SD) of 0.0124, that is 1.24%.**

Let’s run our toy SPY generation process:

– **assuming SD of 4.5% (that mimic the SPY Triple ETFs)**, let’s construct a time series 100 times, and average it.

The** CAGR of the toy SPY is -23%.**

It means that if we bid randomly on the outcome, and our daily expected profit is zero, we should expect -23% annual capital loss every year.

– **assuming SD of 3% (that mimic the SPY Ultra (double) ETFs)**, let’s construct a time series 100 times, and average it.

The **CAGR is -11%.**

It means that if we bid randomly on the outcome, and our daily expected profit is zero, we should expect -11% annual capital decrease every year.

–** assuming SD of 1.5% (that mimic the SPY non leveraged ETFs)**, let’s construct a time series 100 times, and average it.

**The CAGR is -2.7%.**

The loss strongly depends on the SD. However, there is good news here.

**If we have an instrument that is not much volatile, that has a SD of less than 1.5% (as for the SPY), we don’t have to worry too much about the cash position.** This simulation shows that if the probabilities are for us (and not against us), if the Expected profit is above zero, even just slightly above zero, we can go into the position (long or short) full size. **Not going to cash is forgivable, because the maximum we can lose is the -2.7% annual loss of the volatility drag.**

**However, with the triple ETFs the situation is different. The expected profit should compensate for the -23% annual loss of the volatility drag.**

**As the currently popular VIX volatility products (ETFs, futures) can have a Beta of 2 or 3 compared to the SPY**, the cash position should be a frequent position of any strategy that plays the VIX.

**If the expected profit on the next day is not greater than 23%/250= 0.1%, the strategy should favour the cash position for the sake of CAGR.**

**If our utility (goodness) function is not the CAGR, but the Sharpe**, in which the volatility counts too, we would say that this threshold should be even **greater than 0.1% (maybe 0.15% or 0.2%) for a strategy to dislike the cash position.**

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