“So are you selling everything?” was a question I got recently. A fair question since this person had just finished scrolling through two of my recent posts, five charts that should worry equity investors and what that might mean for returns in 2018.
Markets rarely stay at elevated Price-Earnings valuations for long periods. The NIFTY has been at PEs higher than current on only 35 days in 19 years of trading (yes, I counted) while NSE500 has spent just 19 days at valuations at or higher than current. You can find a more detailed analysis in my guest post on capitalmind.in.
Based on all this, my quick-reacting risk-averse lizard-brain (or System 1) tells me the bottom is about to fall out and I should be selling everything and moving to fixed income (FDs or Debt Funds).
But I’m not. Not because I don’t think markets are overvalued but by taking a step back and thinking probabilistically about likely outcomes for 2018 and beyond.
Probabilistic or Bayes Reasoning
Probabilistic reasoning is the process of starting with an “initial” belief then adding “new information” to arrive at a “new and improved” belief. It is also called Bayesian Reasoning after Thomas Bayes, an 18th-century mathematician who came up with a simple yet elegant formula to apply to uncertain situations.
Let’s apply this style of reasoning to the question of whether markets will rise or fall in the next year.
- Start with an initial verifiable belief, call it x: The likelihood that markets will decline sharply, in any given year
- New evidence, current market valuations are much higher than usual i.e. High P/Es
- Since history says high P/Es rarely last, one of two or both need to happen:
- y: Likelihood that markets will correct significantly from here
- z: Likelihood that earnings will rise across the board thus reducing P/Es to reasonable levels
Bayes Theorem allows us to use the above quantities to arrive at a new-and-improved belief
x’: The likelihood that markets will decline sharply in 2018
Bayes Theorem says: x’ = x * y / [(x * y) + z * (1 – x)]
First, let’s put values to x, y and z:
x: likelihood that markets correct significantly in any given year
Since 1999, the NIFTY has given negative annual returns 29% of the time. If we consider negative 10% as a correction, that number falls to 16.5%. The number for NSE500 is similar at 17%
x(NIFTY) = 16.5% | x(NSE500) = 17%
y: likelihood that markets correct significantly given a high PE
This one is trickier because markets spend very little time at high PEs like now.
- Median NIFTY PE is 19.2, 75th percentile is 21.7, 90th is 23.6, Jan 19th, 2018: 27.4
- Median NSE 500 PE is 18.6, 75th percentile is 21.8, 90th is 25.7, Jan 19th 2018: 32.9
We’ll consider the 90th percentile as the threshold for high valuation for this analysis
The NIFTY closed 288 days with a P/E > 23.6. Of these, 235 days resulted in returns < -10% i.e. 82%
The NSE 500 fell more than 10%, 57% of the time when valued more than 25.7x earnings
y(NIFTY) = 82% | y(NSE500) = 57%
z: likelihood that earnings grow significantly thus reducing PEs
As of 19th Jan 2018, NIFTY is at 10,894, PE of 27.44. This implies Earnings of 397 (Price divided by PE)
If the NIFTY is to maintain it’s current level but for PE to reduce to the 90th percentile: 23.6, implies earnings growth of 16%
Over 19 years, the NIFTY has delivered earnings growth of 15%+ in a quarter only 4.7% of the time, 10%+ only 9.8%. Similarly, for the NSE500, that number is 12%
Assuming conservatively that anything above 10% growth will satisfy markets enough to avoid a correction:
z(NIFTY) = 10% | z(NSE500) = 12%
Plugging values of x, y and z into the formula:
x'(NIFTY) = 62% chance of a correction > 10% over the next few months
x'(NSE500) = 49%
Similarly, plugging in likelihood of other levels of correction
Therefore, my revised belief is that there is a strong possibility of markets ending lower than where they started the year and the chances of a correction of more than 10% are significant, but not with as much certainty.
Given steep corrections are rare in general, my strategy over the last month has been:
- Reduce exposure to stocks that have run up far ahead of fundamentals
- Great opportunity to exit low-quality stocks or stocks that worsened fundamentally
- Hold (but not buy more) stocks that have strong fundamentals
- SIP into MFs investing in international markets that are still relatively cheap
Caveat: My implementation of Bayes elegant formula could well be flawed, if you know why, please drop me a note and I’d like to learn where I went wrong
How Bayes’ Rule can make you a better thinker – gizmodo