Thursday, April 26, 2018

Applying the Kelly Criterion as a middle ground between a War-Chest and a Leveraged Portfolio.

This week has been really rough for tech manufacturing and income stocks. But what really saved my portfolio was my margin account which held up while the rest of my portfolio got battered. I really look forward to creating another back-tested equity portfolio in time before my talk.

Anyway, one possible middle ground between the war-chest and the leveraged portfolio is the Kelly Criterion. If you have heard about the casino antics of Ed Thorpe, you will know that he was one of the first to come up with a practical approach towards making bets using the Kelly Formula.

You can find the derivation of the formula for the Kelly Criterion for stocks on this link.

For most of us, we just need to know that the proportion of our war-chest to devote to an investment is equal to ( stock return - risk free rate ) / ( standard deviation of the stock ^ 2 ).

So if perform a back test and find that the STI ETF has provided returns of 3.5% with the risk free rate with a standard deviation of 19%.  We can also derive the risk free rate by using the 10 year local bond current yield of 1.8%.

The Kelly Formula yields (0.035 - 0.018) / (0.19)^2 or 47%.

So you should put 47% of your war-chest into the STI ETF.

Suppose you conduct a back-test and figure out a way to create a REIT portfolio that returns 10% with a standard deviation of 13%, let's see what happens instead when we use the Kelly Formula.

The Kelly Formula in this case yields (0.1 - 0.018) / (0.13)^2 or 485%.

A lot of gamblers suggest using this thing called a Half-Kelly so that your position sizing becomes even more conservative. So even if we take half of 485%, 200% leverage is not as insane as some bloggers make out to be.

As a person who only uses 200% for less than a quarter of my total net worth, I really do not suggest that you use an equation to position size a margin account.

What I am saying is that mathematics may be able to reconcile the differences between a war chest investor and a margin account investor.

Sometimes both can be right.


  1. Thanks for sharing.

    Ed Thorp is an interesting character, Charlie Munger mentioned him once, being able to translate mathematics into the field of Blackjack and then later into Finance when he set up a hedge fund. Being successful in both.

    I am not smart enough to understand the Kelly Criterion though. But seems like it helps to position size based on probability (60% chance leads to about 20% portfolio allocation). There are people who go against the grain on this who have huge portfolio concentration.

    The Kelly formula might be lower if we consider the cost of leveraging also, especially higher costs if we want to leverage beyond 3.5x.

    I was thinking about the Margin Ratio of 2.0 . And it makes sense because if I put in 20k of securities as collateral, by right I should only take 20k margin. If the worst case scenario happens and the stock falls to zero, then (assuming the unlikely situation that collateral remains intact) then I would be able to cover the loss and start at zero.

  2. Also I was thinking whether we could think of the investor as a company.

    With balance sheet & P&L.

    A company with a high growth potential (good investment track record) can probably gear up more compared to a poorer track record investor.

    And if we gear up by margin, how would be look like as a company. Ie, xx% gearing and xx % ROA . And would we invest in this "company".

    This could help decide whether we can take on more margin.

  3. It's basically risk management for how much expected return per unit of variance.

    The volatility or variance plays a large part. If the SD of your margin portfolio spikes to the same as STI i.e. 0.19, the formula more than halves the result to just 227%. Of course the hope is that large REITs with lowish gearing will be less volatile than a bunch of banks & property developers (which is basically the STI).

    Actually if you take a holistic approach, then it's OK. Your overall leverage is only 125% and if your margin method also has a cut loss mark, then it will further mitigate worst outcome.

    The warchest method speaks to sequence of returns risk, where one is unable or unwilling to bear large drawdowns. If you don't have the luxury of time, or a lot of future human capital left, or your portfolio represents past 20 yrs of slog and 90% of FU money, then it makes sense not to be "all-in". Unless you can take a -50% or -60% drawdown without capitulating & selling out, and without affecting your daily living expenses & future plans.

    People like Warren Buffett can take -60% drawdown & sleep like a baby becoz his cash/dividends/coupons/interest is more than enough to last him many decades. Even so, from the way he manages Berkshire with >$100B warchest, he's still a strong believer in having large amounts of dry powder.

    Warchest doesn't have to be cash. It can be the bonds or low-vol portion of portfolio. A no-brainer rules-based disciplined rebalancing approach is basically a warchest method whereby bonds are used to buy equities whenever they go on sale, or become cheaper.