As mentioned in my last post, I stumbled upon a post the other day by RHS Financial, a wealth advisory firm that seems to have an unusual penchant for serious research into quantitative finance.
I find this company’s interest in diving deep into the history of theory and the application of ideas, very refreshing and much more academic than many of the wealth advisors I have come across which tend to be more sales oriented. Yet their posts are still presentable and much more digestible compared to just reading dry academic papers full of equations.
A Brief History
In the post, the author first gives a background of two important figures in information theory and applied mathematics: John Kelly and Edward Thorp.
Kelly was a former WWII pilot who worked for Bell Labs and was considered one of the smartest researchers there. Working with his colleague Claude Shannon who is credited as being one of the fathers of the digital computer and information theory, Kelly studied gambling in the case where the bettor had some inside information. He used the case of a horse race where a bettor with a “private wire” that gave him advanced word of the race’s outcome. Given that the bettor couldn’t be 100% sure that the information he was getting was truthful or not manipulated in some way, it actually made sense for that bettor not to bet all his money on the outcome.
The idea that there was an optimal proportion of one’s capital that should be bet in a scenario like this was quantified and is now called the Kelly Criterion.
Where f is the fraction of her bankroll a gambler should bet, b is the betting odds or payout in the case of a win, p is the probability of winning and q is the probability of losing.
A Kelly Criterion figure greater than one means you should bet more than all your capital, which in the real world would mean you use all your capital and then borrow on top of that, in other words, leverage.
Kelly never got to use his formula as he died young but not long after, a man named Edward Thorp, a math professor who was introduced to Kelly’s mentor Claude Shannon while both working at MIT. Shannon introduced Thorp to Kelly’s criterion when Thorp presented him with a paper which discussed how a player could change the odds of winning blackjack in their favor by counting the cards dealt and betting bigger when there were better cards left in the deck. Combining betting big with the optimal proportion of your money to bet, ended up being the perfect marriage.
Thorp then took his theory to Las Vegas and ended up making a fortune playing blackjack for years there. He ended up publishing a book on his strategy called Beat the Dealer.
Source: Amazon
Thorp eventually stopped betting in casinos and decided to take on Wall St. He co-founded a hedge fund called Princeton Newport Partners. The RHS post described how it turned out:
The results were perhaps the greatest risk-adjusted returns any hedge fund had ever delivered before or since. Between 1969 and 1988 Princeton Newport had a compound annualized return of 19.1% vs. the S&P 500’s 10.2%. What’s more, over its two decades in operation, PNP only lost money in three months, and its returns were completely uncorrelated with those of the stock market or any other risky asset.
That’s Great, So Why Does This Matter?
Things start to get interesting when RHS used these ideas to delve into the Kelly Criterion as it applies to the returns of the S&P 500, which any retail investor can now easily put their money into and leverage through an ETF. The modified Kelly Criterion for stock market return was as follows:
With the risk free rate being that of short term government bonds and volatility being the standard deviation of returns during the period examined.
Using the starting point of when the first ETF was traded in 1993, the authors took a look at the data set of returns. The first was the S&P with no leverage, which returned 9.28% annually between 1993 and 2017. This was assumed to be normally distributed and 9.28% assumed to be the expected return over this period.
Source: RHS Financial
When you plug in the numbers for the Kelly Criterion in this case, it shows that the optimal leverage figure is 237%, RHS then plotted the return of the S&P with that level of leverage for $1 invested in 1993.
Source: RHS Financial
The Kelly investor would have completely lost their lead to the unlevered investor twice over the years following both the dot-com bust and the 2008 financial crisis before finally finishing in May 2017 with a terminal wealth of $18.88, an annualized return of 12.84%.
237% leverage for about 3-4% great return doesn’t sound that great considering all the volatility you have. However the RHS authors offered an alternative: invest instead in a lower volatility portfolio. The low volatility portfolio they used was the S&P Low Volatility 100, for which they used the Invesco S&P 500 low volatility ETF SPLV as well as an ETF for long term government bonds, the iShares 20+ year treasury bond ETF TLT. This portfolio returned 9.36% over the same period with even lower volatility.
The Kelly Criterion for this low volatility portfolio would be 10.38, meaning if you had $1000, you would borrow $9,380 to meet the criterion. Although volatility would be exceedingly high with this portfolio, producing volatility 4 times that of the S&P 500, the returns would end up being an annualized rate of 45.44%. Take a look at the plotted returns over the period examined below.
Source: RHS Financial
That $1 invested in 1993 would have become $9,067 by 2017. That’s a return similar to the 41% return you would have gotten had you invested with Amazon at their IPO which return 41% annually from 1997 to 2018.
Source: CNBC
Be Creative In Applying These Lessons
The author cautions that these are not realistic portfolios due to practical matters such as the rates that brokers charge for margin and limits on leverage etc. However this is limited thinking. As I pointed out in my last post, leverage can also come from real estate, especially if you are renting your properties to cover part or all of the costs.
Let’s say for example you have $100,000 to invest, rather than putting it in the market with no leverage, use that $100,000 to buy a $500,000 which you rent in a decent market where you can see home price appreciation of about 4% a year. Applying patience and discipline, after 5 years the home value will have grown to $608,000 about a 100% return if we assume some costs as well. At this time, you can re-lever up through re-financing. That would give you about $87,000 in cash which you can then put into the low volatility portfolio to watch grow. Let’s assume you just leave it there and let your home value and investment grow another 10 years.
In this case you end up with about $450,000 in equity in the home and $212,000 in the low volatility portfolio. On the original investment of $100,000 that produces a return of about 13.4%. It’s not the 45% above but it’s a simple example of using leverage and a simple portfolio to increase your returns.
Conclusion
We may be looking at a period of low interest rates and low growth for some time. This is a distinct advantage for those willing to consider and use leverage for their investments. There has never been such easy access to low risk portfolios and backdoor leverage for the average investor. Just about anyone can achieve the 13.4% return I described about with knowledge and discipline.
The option of using preferential rates on real estate to leverage investments is an enticing one that I would like to continue to explore in more detail in more upcoming posts.
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