Incorporating Risk Skew into Investing

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secondopinion
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Incorporating Risk Skew into Investing

Post by secondopinion »

I am posting this more for discussion than a question.


Let us turn toward singleton stocks.

Many here are averse to holding a few singleton stocks. Why? History has shown that singleton stock returns are very often to be positively skewed (unlikely massive outperformance, but likely underperformance); also, history has shown that holding a large collection of stocks reduces both this skew and volatility. However, some still do hold singleton stocks. Why? If one supposes that expected returns do not differ and the volatility is higher; it would seem that holding singleton stocks is a bad choice. But why are some comfortable with the prospect of holding singletons? Two possibilities exist:
  • They believe they can pick investments with a better expected return.
  • They seek positive risk skew regardless of the returns.
The first reason is very debatable if it is even possible, but the second reason can be definitely achieved. That is, those who are seeking the positive risk skew can and are willing to pay the price of more volatility, despite it could do nothing to benefit expected returns. Those positive-skew seekers can optimize their portfolio achieving the best utility given expected return, volatility, and risk skew by adding singleton stocks.

I will leave research of this to the reader to find this skew.


Now, let us turn toward singleton high quality corporate bonds. It is more or less a repeat, so just note that the skew is negative in this case instead of positive.

Many here are averse to holding a few singleton high quality corporate bonds. Why? History has shown that holding a large collection of bonds reduces both skew and volatility. But here, singleton high quality corporate bond returns are very often to be negatively skewed (likely outperformance, but unlikely major underperformance). However, some still do hold singleton bonds. Why? If one supposes that expected returns do not differ and the volatility is higher; it would seem that holding singletons is a bad choice. But why are some comfortable with that prospect as well? Two possibilities exist:
  • They believe they can pick investments with a better expected return.
  • They seek negative risk skew regardless of the returns.
The first reason is very debatable if it is even possible, but the second reason is definitely achieved. That is, those who are seeking the negative risk skew are willing to pay the price of more volatility, despite it could do nothing to expected returns. Those seekers can optimize their portfolio achieving the best utility given expected return, volatility, and risk skew by adding singleton bonds.

To illustrate this negative skew, suppose that one bond index fund has bonds that all have the same maturity, all have the same yield, and all have a default risk of 5% instantly (given independence, that is; but the argument is still reasonable). Suppose the fund closes after they all mature. Picking the index fund will likely give you about 95% of the yield and principal regardless by assumption. However, another investor buys only 5 such bonds and does the same. They have about a 77.38% chance of having no defaults, so they have about a 77.38% chance of outperformance. Massive underperformance is not the norm but it is possible.


So, let us talk about "play money". Aside from the fact that I detest the notion of risking money just for the fun of it, I understand it as money invested that deviates majorly from general indexes.

When we restrict ourselves to the primary indexes, we leave no room for adjustment for skew; we can really only modify expected return and volatility. To those not interested in or averse to skew, they can obtain a mostly efficient portfolio just by staying with these indexes.

So then there money invested to change the skew for the skew-seeking investors, and the optimal portfolio does not only stay in the indexes alone. It shows up as singleton stocks, singleton bonds, certain option strategies, bizarre investment alternatives, etc. When you consider investing with the acceptance of skew, you can definitely see why these deviations do occur.


Maybe this is a strange post, but I see that a lot of discussion can be explained by risk skew and the seeking for it.
Passive investing: not about making big bucks but making profits. Active investing: not about beating the market but meeting goals. Speculation: not about timing the market but taking profitable risks.
000
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Re: Incorporating Risk Skew into Investing

Post by 000 »

secondopinion wrote: Wed Sep 22, 2021 3:37 pm I am posting this more for discussion than a question.
It gives a certain appeal to something like a 20 stock portfolio. Having even just 5% in what becomes a huge winner and never rebalancing might be a lot more emotionally rewarding than lagging the index is emotionally punishing.

Why would someone want negative skew though? How many investors get a thrill because their corporate bonds didn't default??

I wonder if it's possible to pursue skew in systematic ways. Perhaps some options strategies could be used as systematic skew seeking behavior.

I hold some individual stocks in the portfolio, about 6%, but the explicit reason was more due to dissatisfaction with the stocks dominating indices and with the construction of, say, SCV funds. Although positive skew is a partial reason I was willing to do that as opposed to buying individual corporates.
Topic Author
secondopinion
Posts: 6008
Joined: Wed Dec 02, 2020 12:18 pm

Re: Incorporating Risk Skew into Investing

Post by secondopinion »

000 wrote: Sat Oct 16, 2021 1:49 am
secondopinion wrote: Wed Sep 22, 2021 3:37 pm I am posting this more for discussion than a question.
It gives a certain appeal to something like a 20 stock portfolio. Having even just 5% in what becomes a huge winner and never rebalancing might be a lot more emotionally rewarding than lagging the index is emotionally punishing.

Why would someone want negative skew though? How many investors get a thrill because their corporate bonds didn't default??

I wonder if it's possible to pursue skew in systematic ways. Perhaps some options strategies could be used as systematic skew seeking behavior.

I hold some individual stocks in the portfolio, about 6%, but the explicit reason was more due to dissatisfaction with the stocks dominating indices and with the construction of, say, SCV funds. Although positive skew is a partial reason I was willing to do that as opposed to buying individual corporates.
To the first, positive risk skew can be rewarding emotionally to some. That is why risk tolerance and goals must also include the risk skew. However, the more stocks you include the less positive risk skew will be present. Generally, positive risk skew is for those who are very likely to meet their modest goals but want to aim for the stars; too much volatility would be hazardous to meeting their modest goals (as it could go awry), so having considerable positive risk skew is the correct way to do so.

To the second, negative risk skew is not just for bonds; but like how most stocks carry positive skew, most bonds carry negative skew. But by using options, one can change stocks to be negatively skewed. Negative skew is not thrilling by definition, but there is likely outperformance versus positive skew's likely underperformance. Most people who take negative skew have a lot of financial stuffing but not exactly the desire to massively outperform; they want likely outperformance instead. Just merely increasing volatility does not improve the odds.

In short, positive skew fight the odds and negative skew go with the odds.

Options are the best way to massively change the portfolio's risk skew (as well as taking volatility and gamma/theta risk). And singleton options are not the only way to do so. You can have option strategies that imperfectly hedge stocks (like OTM put butterflies) that carry a lot of positive skew and keep likely underperformance limited, but they are definitely not likely to be profitable. But with positive skew, it can be potentially rewarding (with hedges, this means counteracting loss by a large amount and gives considerable dry powder to reinvest, while not expending much capital to do so). The trick is to avoid increasing risk by much while obtaining skew (unless one lives for the "saw"). Most of the time, debit positions are positive skew and credit positions are negative skew (but more accurately, it is the percentage of being profitable that drives most of it). Some option strategies just add volatility without changing the skew, so you have to be careful before you enter any position.

Lastly, most tilts with stocks are positive skewing and sometimes increase volatility (large cap tilts might be the oppose though). If positive risk skew is desired up to the point of taking more volatility, then by all means include some individual stocks or tilt. Research will likely not surface the superior returning stocks, but it will often identify the volatility and risk skew profile.
Passive investing: not about making big bucks but making profits. Active investing: not about beating the market but meeting goals. Speculation: not about timing the market but taking profitable risks.
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