Do You Want To Be “The House”?

We would like to welcome Lake Hill Capital Management as our newest contributor to the CBOE Options Hub. 

Lake Hill Capital Management is a private firm specializing in quantitative and relative-value trading in derivatives markets.  Lake Hill has partnered with institutions and high net-worth families to provide unique strategies. Lake Hill applies a very disciplined and research driven investment process. Alpha is generated by providing liquidity and harvesting systematic structural edge in various exchange traded markets.  The firm invests significant resources into state-of-the-art technology and computational systems.  Lake Hill combines technical knowhow with practical hands-on experience to stay competitive in an ever-evolving marketplace.  Thank you Justin Golden, Managing Partner with Lake Hill Capital for coordinating these blog pieces.

Who wouldn’t want to own a roulette wheel!?  Having the odds in your favor all of the time sounds pretty appetizing. Just collect the “vig” day in and day out. Easy money, right?  WRONG.

It is common knowledge that owning a casino, or being “the house”, has its advantages. “The house always wins” as the saying goes. The truth is that while the edge is slightly tipped in the house’s favor, there is significant volatility that comes with it.

roul wheel

On a roulette wheel, the edge to the house is small. Using the European-style wheel pictured above with only one green outcome (otherwise known as Number 0), the probability of black or red coming up is 18 out of 37, or 48.6%. Correctly betting on black or red yields an even money payout despite the odds of winning being less than 50%. The difference between the payout and the probability is one way of describing the “house’s edge.”

We can calculate the edge to the house using an example of a player betting on a black number:

House Edge = probability of black NOT coming up less the probability of black coming up

House Edge = 19 (reds + green numbers) / 37 (all numbers)  –  18 (black numbers) / 37 (all numbers)

House Edge = +2.7%

A player betting black will have at 48.6% chance of winning leaving the remaining 51.4% chance to the house. Even with that small advantage, the short-term volatility of profit and loss can be significant. In order to realize the edge the house has to be well capitalized, patient, and needs lots and lots of spins.

The charts below sample the theoretical profit and loss of 1000 spins of a roulette wheel where the player can only bet on black or red. The house has a 51.4% chance of winning $1 per spin.

lh chart 1

Figure 1: Random sample of PnL from 1000 spins of a roulette wheel with a $1 wager on black or red. The house has a 51.4% chance of winning $1 per spin. 

lh 2 chart

Figure 2: Random sample of PnL from 1000 spins of a roulette wheel with a $1 wager on black or red. The house has a 51.4% chance of winning $1 per spin. 

The outcomes are quite different with Figure 1generating an 80% return and Figure 2 generating a 20% loss over the same period of time. The edge didn’t change between these two examples. The process was exactly the same.

Even though the house had the same edge with each bet on black or red, if you didn’t know the risk of loss, as with Figure 2, you might think there is something wrong with your wheel.

What can we learn from this and can it be translated into how we think about investments?

An important part of investing is being able to get comfortable with the variability of returns, along with the depth and length of draw-downs. Having some knowledge of this, in advance, helps to “right-size” the investment and avoid big gaps between expectation and reality.

If you believe you have identified a small edge in an investment you still need to consider the volatility of returns. If the investment is made at the wrong time and the outcome is negative even though you still have an edge, how will you respond? Can you tolerate the unpredictability of returns without liquidating, or worse, being forced to liquidate? These are the types of questions worth addressing before making an investment.