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@David Harper CFA FRM

Rebalancing as a portfolio strategy is also a short volatility strategy which produces a long run volatility risk premium. Investors who do not rebalance (those who own 100% of the market) are long volatility risk and lose the long-run volatility risk premium.
Chapter 7 ( Factors)

#### David Harper CFA FRM

##### David Harper CFA FRM
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Hi @Jaskarn These assertions by Ang are based on his elaboration in Chapter 4; I have attached the section here

Ang compares a buy-and-hold strategy to a rebalancing strategy where the trader rebalances to maintain 60% equity + 40% bonds:
"In Figure 4.9, Panel D, the buy-and-hold strategy is the completely passive straight line. The rebalancing strategy is an active strategy that transfers payoffs from the extreme low and high stock realizations (Suu and Sdd) to the middle stock realization (Sud = Sdd). Rebalancing does this by selling when stock prices are high and buying when stock prices are low. Short volatility positions do exactly the same. A call option can be dynamically replicated by a long stock position and a short bond position. This buys equity when stock prices rise and sells equity when stock prices falls. A short call option does the opposite: a short call position is the same as selling when equity prices rise and buying when they fall. Likewise, a short put is also dynamically replicated by selling equity when prices rise and buying when prices fall. These are exactly the same actions as rebalancing."-- Ang, Chapter 4, page 139
... put more simply (I think!) the rebalance strategy is short volatility because it sells (buys) when equity prices increase (decrease) and therefore "bets against" momentum (i.e., further increase or decrease). Short volatility is replicated by selling options (aka, short position gamma): the option seller collects the premium and profits if volatility is low; i.e., if realized volatility is less than implied volatility at the sale. The potentially confusing idea IMO is that the volatility risk premium is negative instead of positive:
"Because rebalancing is short volatility, it automatically earns the volatility risk premium. In our example, volatility is constant (the stock volatility is equal to 0.75), but in reality volatility varies over time. Volatility is a risk factor and earns a negative risk premium. An investor collects the volatility risk premium by selling options or by being short volatility. I discuss this further in chapter 7." -- Chapter 4, page 141
... and we need to jump to Chapter 7, perhaps, to fully grok why Ang is saying that the volatility risk factor earns a negative risk premium, in contrast to our typical expectation that risk premiums are positive compensation for incurred risk factors. But if you followed the market in 2018, this is not strange at all (!), as short vol strategies exploded in popularity in early 2018 before they led to a crashing unwind:
"Stocks are not the only assets to do badly when volatility increases. Volatility is negatively linked to the returns of many assets and strategies. Currency strategies fare especially poorly in times of high volatility. We shall see later that many assets or strategies implicitly have large exposure to volatility risk. In particular, hedge funds, in aggregate, sell volatility (see chapter 17).

Investors who dislike volatility risk can buy volatility protection (e.g., by buying put options). However, some investors can afford to take on volatility risk by selling volatility protection (again, e.g., in the form of selling put options). Buying or selling volatility protection can be done in option markets, but traders can also use other derivatives contracts, such as volatility swaps. Investors are so concerned about volatility, on average, that they are willing to pay to avoid volatility risk, rather than be paid to take it on. Periods of high volatility coincide with large downward movements (see Figure 7.3) and assets that pay off during high volatility periods, like out-of-the-money puts, provide hedges against volatility risk.

We often think about assets having positive premiums—we buy, or go long, equities, and the long position produces a positive expected return over time. Volatility is a factor with a negative price of risk. To collect a volatility premium requires selling volatility protection, especially selling out-of-the-money put options. The VIX index trades, on average, above volatilities observed in actual stocks: VIX implied volatilities are approximately 2% to 3%, on average, higher than realized volatilities. Options are thus expensive, on average, and investors can collect the volatility premium by short volatility strategies. Fixed income, currency, and commodity markets, like the aggregate equity market, have a negative price of volatility risk." -- Chapter 7, page 221

Hi @Jaskarn Good for you for thinking it out and challenging the idea, these are difficult. Please notice that we cannot easily compare volatility to the strike price; e.g., it's hard to compare K = $50.00 to σ = 25.0%. Say you write (sell) me an out-of-the-money (OTM) put for a price (premium) of$5.00 based on an implied volatility of 30.0% (after all, the sale price [i.e., the option premium] implies the implied volatility. This is the definition of an implied volatility). You are then short volatility (your position vega is negative) and you are short gamma (your position gamma is also negative). If the realized volatility is subsequently greater than (lower than) 30.0%, then the price of the option (ceteris paribus) will increase and, because you are short the option, you will experience a mark-to-market loss (gain) just as your counterparty, which is me David Harper who purchase the option and who is long vega and long gamma, will experience a M2M gain (loss). I hope that's helpful!