Since the market has been through some numerous mini turmoils in since the beginning of 2016, I feel the urge to write about the likelihood of a 10% decline in S&P this year. Since today, the S&P YTD return sits at ~(4.9)%. While the mainstream media (Marketwatch, Bloomberg, CNNMoney etc.) flooded the market with recession-prompting articles, it’s worth noting that the volatility index (VIX) is still within a relatively reasonable range. Anyways, back to the topic.
As a rough rule of thumb, I would just look at the SPX -10% OTM December put. The delta is approximately the probability that the option expires in the money. Let’s assume the delta is 0.20, this means the market is pricing in about a 25% chance that the 10% OTM put for December 2016 expires in the money, in other words, a 25% chance the market is down 10% by year end.
RESULTS:
The probability the market finishes the year below some threshold KK (in our case 180 for SPY or 1800 for SPX) is
p[S≤K]=1−CS(K,K+ΔK)ΔKp[S≤K]=1−CS(K,K+ΔK)ΔK
Where CS(K,K+ΔK)CS(K,K+ΔK) is the value of the call spread at strikes K,K+ΔKK,K+ΔK expiring on Dec 30. I looked up SPY to find the call values
C(K=180)=$19.41,C(K=185)=$15.47C(K=180)=$19.41,C(K=185)=$15.47 , which leads to
p[10% drop]=21%
NOTES:
You’ll need to make some adjustments for dividend payments, but the “mean” would essentially be the spot price, the “test” price is 10% OTM strike price. You can get the standard deviation from the implied volatility. And you should also make some adjustments for skewness and kurtosis to control for the fact that SPX returns don’t actually follow a normal distribution. Lastly you also need to adjust for the fact that SPX can’t trade negative
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