Short Selling (Part 1)

This is a 2-part post about short selling. It deals with the theory and portfolio effects first, then looks at recent performance of portfolios short stocks and bonds in the US markets.

INTRODUCTION
The layman’s understanding may be that holding a short position is just the opposite of holding a long position. If a shock goes up by 10%, the investor gets +10% return if they are long and -10% return, if they are short. This may be true for a very short holding period (less than a day), but when holding for a longer time, the performance of a short position is not the opposite of a long position. There are multiple factors affecting short selling as I will explain in detail below.

There’s a reasonable introduction to short selling in Investopedia, here. However, it contains some inaccuracies and perhaps slightly misleading statements. Some may have been true when interest rates were at zero, but are not true anymore. At the outset the authors state that: “Short selling [is an] investment activity in which the investor borrows securities and sells them in the hopes of then purchasing the securities at a lower price in the future.” As we’ll see below an investor can be perfectly happy short selling when he expects the price of the underlying to be flat or even go up. This may be true even holding the short position outright, not as a part of a hedging strategy.

RETURNS DECOMPOSITION

It may be worthwhile to start from the decomposition of returns to a long position and a short position. As we see in the table below, holding a short position is accompanied by several factors that do not exist if we just go long. The positive (negative) sign means that the return of the position is positively (negatively) correlated with the change of the line item. Zero sign means that the effect does not exist for this specific line item. I’m splitting the effect between investments for futures and stocks/ETFs, as there are some material differences between these types of instruments when shorting them. The difference between stocks and ETFs consists mainly of the management fee. In order to simplify matters, in all cases I’m assuming the portfolio is fully invested, i.e. an exposure of +100% for a long position and -100% for a short position.

Fig. 1.1 A summary of effects impacting a long and a short position

THE LONG POSITION
The effects while holding a long position is rather straightforward: you get the change in the underlying minus the management fee – in case of the ETFs. In case of dividend or interest paying instruments, such as stocks or bonds, the change in the underlying is the total return: price change + dividends or interest. Simple enough.

THE SHORT POSITION
The effects impacting the short position are a bit more complicated.

1) The change of the underlying
We have the opposite effect of the long position here: when your investment goes up, your portfolio value goes down by the same percentage. Instead of receiving dividends or interest from the underlying instrument, you need to pay it to the owner of the instrument. Hence the negative signs in the table: your portfolio’s value is negatively correlated with the return of the underlying instrument.

However, the simplicity of the calculations breaks down after the first change in value of the underlying. Let’s explain it using an example. Let’s consider what happens to portfolio value and its exposure to the underlying instrument when the price change in the underlying is “proper” for both strategies, up for the long strategy and down for the short strategy. In the case of the long strategy, both the value of the underlying and the value of the portfolio change in tandem from $100 to $110. The exposure stays at 100% of portfolio. However, in the short portfolio, the changes go in the opposite directions: as the underlying drops from $100 to $90, portfolio value increases from $100 to $110. The exposure of the portfolio drops to 82%.

Fig. 1.2 The impact of price changes on a long and short position

This leaves the portfolio manager with a dilemma: to rebalance or not to rebalance. Choosing not to rebalance has three potential issues:
A) The exposure is never -100% as intended
B) It opens the possibility of catastrophic losses
C) It limits the upside to +100%

A) If we choose not to rebalance, the exposure of the portfolio to the underlying instrument is variable and at the mercy of the price changes. It will (almost) never be 100% as originally intended. This is why the short (inverse) ETFs (such as SH, PSQ or TBX) have to rebalance daily, in order to always offer the potential investors -100% exposure.

B) Not rebalancing opens the possibility of catastrophic losses of the total value of the portfolio, or even more. The reason is that the underlying can increase in price by 100% or more, resulting not only in wiping out the whole investment capital, but potentially putting the investor in debt. On the contrary, rebalancing requires a gradual reduction of the exposure – buying back part of the short position. This reduces the risk and likelihood of the loss of capital.

C) It is often said that the maximum profit while shorting is 100%, as the value of the underlying cannot go below zero. However, if one decides to rebalance, the upside from shorting is practically unlimited. The table below presents the potential profits from shorting in two versions: non-rebalanced and rebalanced at 1% intervals, assuming the price of the underlying goes down monotonically:

Fig. 1.3 The impact of rebalancing on realized short selling profits


As we see, rebalancing your shorts all the way down can (theoretically) offer 9.8x return when your underlying goes down by 90% and 94x return, when it goes down by 99%.

If it all looks too good to be true, with three distinct advantages of rebalancing, that’s because it is. No investment goes down in a straight line and short selling suffers from the so-called Volatility Slippage.

2) Volatility Slippage
Let’s return to the example where the underlying went down by 10%, the value of the portfolio went up by 10% resulting in an exposure of 82%. In order to bring the exposure back to 100% the investor needs to sell short additional 18% of the portfolio’s value. However, the sale is being done at lower prices than originally. So, the investor needs to sell low to rebalance. What happens when the price of the underlying goes back up to the original price? The rebalancing requires a repurchase (covering) of some of the short position. The volatility slippage is thus a drag on the portfolio’s performance. The investors needs to sell low and buy high – the opposite of the usual trader’s strategy.

How much is the drag worth? It depends on the underlying instrument’s volatility. To cut things short and not to bother the reader with the equations, it suffices to say that for the -1x short position the volatility drag is approximated by the variance of the underlying instrument. So, for the stocks with volatility of 20% annually, the volatility drag amounts to 4% p.a. Bonds with 8% volatility suffer from a 0.64% volatility drag annually. This is not good. Even if we manage to nail the decline in stocks and they go down by 10% in a year, volatility drag will eat as much as 40% of the profits we made. Can we count on some additional help? Yes, we can.

3) DOUBLE the risk free rate
Recent increase in Fed Funds and Treasury Bills yields towards 5% offers investors an opportunity to capitalize on them not only by holding cash that finally earns decent interest, but also juicing up profits from shorting. Short selling position has a positive financing of double the risk-free rate embedded. How so?

First of all, in order to short a financial instrument, you don’t need to deploy your own capital. Well, with caveats. You need to reserve some portion of your capital as margin, but it is quite small. For example, at the moment of writing you need to reserve a margin of just 5.3% for the S&P 500 futures (tickers ES and MES) and 2.6% for the Ultra 10-year bond futures (ticker TN). The rest can be invested in at the risk-free rate, yielding ~5% for your portfolio.

Secondly, the same risk free rate is embedded in the prices of futures. In order to have a parity pricing between holding the position outright and holding a position consisting of futures + T-bills, futures price needs to take T-bill rate into account. They will be priced high when launched and slowly converge to the price of the instrument underlying the futures at expiry.

There you have it: at current risk free rate, you get 10% financing help when holding a short position. However, there are some deviations from this rule. We will discuss them in more detail in points 4) and 5) in Part 2 of the series.s

This is getting slightly complicated at this moment. Total profit from a short position depends not only on the total return of the shorted instrument, but also on the whether we rebalance or not. When we do, the result depends on the volatility of the instrument. Additionally, we get help from the financing rate. In order to put this all together, let’s look at the following table. It presents the results of a short portfolio for different levels of volatility (5-25%) and total return (from -10% to +5%) of the underlying instrument.

Fig. 1.4 Return to a short portfolio for different levels of return and volatility of the underlying instrument

As we see, a short position will result in positive return not only when the price of the underlying goes down, but also when it is unchanged and even when it goes up. As an example, portfolio being short stocks with 20% volatility will yield 6% return when they are unchanged: 10% from 2 x risk free rate and -4% from the volatility slippage.

The following table tries to visualise a different dillema: for a given change in the underlying instrument and given volatility, is it more profitable to enter a short or a long position?

Fig. 1.5 Return difference between a short and a long portfolio for different levels of return and volatility of the underlying instrument

As we see, the line of indifference lies at slightly positive returns of the underlying: for an instrument with 20% volatility a positive 3% return of the underlying yields the same profits for the long and the short position. For an instrument with 10% volatility a 4.5% positive return in the underlying results in identical returns for the long and short positions.

We can establish in principle what the return of the underlying needs to be, in order for the investor to be indifferent between a long and a short position. For the non-rebalanced portfolios the expected return of the instrument under consideration needs to exceed the risk free rate. This makes intuitive sense: if an investment yields higher return than T-Bills, we go long. If the return is lower, we sell the investment short and invest the proceeds at the risk free rate. For a rebalanced portfolio the situation is a bit more complex, as we lose money to the volatility slippage. In order to go short the expected return of the underlying needs to be lower than risk free rate minus half of variance.

This concludes Part 1. In Part 2 we will look at the less pronounced effects 4-6 and some real-life examples from the recent past.

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