Call Overwriting & Put Writing
Derivatives-based Portfolio Solutions
OPTION IMPLIED VOLATILITY IS USUALLY OVERPRICED
The implied volatility of options is on average 1-2 pts above the volatility realized over the life of the option. This ‘implied volatility premium’ is usually greater for indices than for single stocks. As we can see no reason why these imbalances will fade, we expect call overwriting to continue to outperform on average. The key imbalances are:
CALL OVERWRITING BENEFITS FROM SELLING EXPENSIVE VOLATILITY
Short-dated implied volatility has historically been overpriced due to supply and demand imbalances. In order to profit from this characteristic, a long investor can sell a call against a long position in the underlying of the option. Should the underlying perform well and the call be exercised, the underlying can be used to satisfy the exercise of the call. In the real world As equities should be assumed to offer a positive return over time (the equity risk premium,an assumption that does not hold in the risk-neutral world) it is best in practice to overwrite with a slightly OTM option to reduce the probability of the option sold expiring ITM.
Call overwriting is a useful way to gain yield in range trading markets
If markets are range trading, or are approaching a technical resistance level, then selling a call at the top of the range (or resistance level) is a useful way of gaining yield. Such a strategy can be a useful tactical way of earning income on a core strategic portfolio, or potentially could be used as part of an exit strategy for a given target price.
Selling at target price enforces disciplined investing
If a stock reaches the desired target price, there is the temptation to continue to own the strong performer. Over time a portfolio can run the risk of being a collection of stocks that had previously been undervalued, but are now at fair value. To prevent this inertia diluting the performance of a fund, some fund managers prefer to call overwrite at their target price to enforce disciplined investing, (as the stock will be called away when it reaches the target). As there are typically more Buy recommendations than Sell recommendations, call overwriting can ensure a better balance between the purchase and (called away) sale of stocks.
CALL OVERWRITING PROFILE IS SIMILAR TO PUT UNDERWRITING
Call overwriting could be considered similar to stock replacement with a short put (or put underwriting). Both call overwriting and put underwriting attempt to profit from the fact that implied volatility, over time, tends to be overpriced. While selling a naked put is seen as risky, due to the near infinite losses should stock prices fall, selling a call against a long equity position is seen as less risky (as the equity can be delivered against the exercise of the call).CALL OVERWRITING IS BEST DONE ON AN INDEX
Boosters (1×2 call spreads) are useful when a bounce-back is expected
If a near zero cost 1×2 call spread (long 1×ATM call, short 2×OTM calls) is overlaid on a long stock position, the resulting position offers the investor twice the return if the equity increases up to the short upper strike. For very high returns the payout is capped, in a similar way as for call overwriting. Such positioning is useful when there has been a sharp drop in the markets and a limited bounce back to earlier levels is anticipated. The level of the bounce back should be in line with or below the short upper strike. Typically, short maturities are best (less than three months) as the profile of a 1×2 call spread is similar to a short call for longer maturities.
Many investors call overwrite on single stocks. However, single-stock implied volatility trades more in line with realized volatility than index implied volatilities. The reason why index implied volatilities are more overpriced than single-stock implied volatilities is due to the demand from hedgers and structured product sellers. Call overwriting at the index level also reduces trading costs (due to the narrower bid-offer spread). The CBOE has created a one-month call overwriting index on the S&P500 (BXM index), which is the longest call overwriting time series available. It is important to note that the BXM is a total return index; hence, it needs to be compared to the S&P500 total return index (SPTR Bloomberg ticker) not the S&P500 price return (SPX Bloomberg ticker).LOWER DELTA REDUCES BENEFIT OF EQUITY RISK PREMIUM
Call overwriting performance varies according to equity and volatility market conditions
On average, call overwriting has been a profitable strategy. However, there have been periods of time when it is has been unprofitable. The best way to examine the returns under different market conditions is to divide the BXM index by the total return S&P500 index (as the BXM is a total return index).
Call overwriting underperforms in strong bull markets with low volatility
Since the BXM index was created, there have been seven distinct periods, each with different equity and volatility market conditions. Of the seven periods, the two in which returns for call overwriting are negative are the bull markets of the mid-1990s and middle of the last decade. These were markets with very low volatility, causing the short call option sold to earn insufficient premium to compensate for the option being ITM. It is important to note that call overwriting can outperform in slowly rising markets, as the premium earned is in excess of the amount the option ends up ITM. This was the case for the BXM between 1986 and the mid-1990s. It is difficult to identify these periods in advance as there is a very low correlation between BXM outperformance and the earlier historical volatility.
We note that while profits should be earned from selling an expensive call, the delta (or equity sensitivity) of the long underlying short call portfolio is significantly less than 100% (even if the premium from the short call is reinvested into the strategy). Assuming that equities are expected to earn more than the risk free rate (ie, have a positive equity risk premium), this lower delta can mean more money is lost by having a less equity-sensitive portfolio than is gained by selling expensive volatility. On average, call overwriting appears to be a successful strategy, and its success has meant that it is one of the most popular uses of trading options.OVERWRITING WITH NEAR-DATED OPTIONS HAS HIGHEST RETURN
Near-dated options have the highest theta, so an investor earns the greatest carry from call overwriting with short-dated options. It is possible to overwrite with 12 one-month options in a year, as opposed to four three-month options or one 12-month option. While overwriting with the shortest maturity possible has the highest returns on average, the strategy does have potentially higher risk. If a market rises one month, then retreats back to its original value by the end of the quarter, a one-month call overwriting strategy will have suffered a loss on the first call sold but a three-month overwriting strategy will not have had a call expire ITM. However, overwriting with far-dated expiries is more likely to eliminate the equity risk premium the investor is trying to earn (as any outperformance above a certain level will be called away).BEST RETURNS FROM OVERWRITING WITH SLIGHTLY OTM OPTIONS
While overwriting with near-dated expiries is clearly superior to overwriting with far-dated expiries, the optimal choice of strike to overwrite with depends on the market environment. As equities are expected, on average, to post a positive return, overwriting should be done with slightly OTM options. However, if a period of time where equities had a negative return is chosen for a back-test, then a strike below 100% could show the highest return. Looking at a period of time where the SX5E had a positive return shows that for one-month options a strike between 103%-104% is best. For three-month options, the optimal strike is a higher 107%-108%, but the outperformance is approximately half as good as for one-month options. These optimal strikes for overwriting could be seen to be arguably high, as recently there have been instances of severe declines (TMT bubble bursting, Lehman bankruptcy), which were followed by significant price rises afterwards. For single-stock call overwriting, these strikes could seem to be low, as single stocks are more volatile. For this reason, many investors use the current level of volatility to determine the strike or choose a fixed delta option (i.e. 25%).OVERWRITING REDUCES VOLATILITY AND INCREASES RETURNS
While selling an option could be considered risky, the volatility of returns from overwriting a long equity position is reduced by overwriting. This is because the payout profile is capped for equity prices above the strike. An alternative way of looking at this is that the delta of the portfolio is reduced from 100% (solely invested in equity) to 100% less the delta of the call (approx. 50% depending on the strike). The reduced delta suppresses the volatility of the portfolio.ENHANCED CALL OVERWRITING IS POSSIBLE BUT DIFFICULT
Benefit of risk reduction is less impressive if Sortino ratios are used to measure risk
We note that the low call overwriting volatility is due to the lack of volatility to the upside, as call overwriting has the same downside risk as a long position. For this reason, using the Sortino ratio is likely to be a fairer measure of call overwriting risk than standard deviation, as standard deviation is not a good measure of risk for skewed distributions. Sortino ratios show that the call overwriting downside risk is identical to a long position; hence, call overwriting should primarily be done to enhance returns and is not a viable strategy for risk reduction.
We expect optimal strike for overwriting to be similar for single stocks and indices
While this analysis is focused on the SX5E, the analysis can be used to guide single-stock call overwriting (although the strike could be adjusted higher by the single-stock implied divided by SX5E implied).
Enhanced call overwriting is the term given when call overwriting is only done opportunistically or the parameters (strike or expiry) are varied according to market conditions. At the index level, the returns from call overwriting are so high that enhanced call overwriting is difficult, as the opportunity cost from not always overwriting is too high. For single stocks, the returns for call overwriting are less impressive; hence, enhanced call overwriting could be more successful. An example of single-stock enhanced call overwriting is to only overwrite when an implied is high compared to peers in the same sector. We note that even with enhanced single-stock call overwriting, the wider bid-offer cost and smaller implied volatility premium to realized means returns can be lower than call overwriting at the index level.
Enhanced call overwriting returns is likely to be arbitraged away
Should a systematic way to enhance call overwriting be viable, this method could be applied to volatility trading without needing an existing long position in the underlying. Given the presence of statistical arbitrage funds and high frequency traders, we believe it is unlikely that a simple automated enhanced call overwriting strategy on equity or volatility markets is likely to outperform vanilla call overwriting on an ongoing basis.
Put & Call Writing
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