One of the most difficult things about managing an investment portfolio is determining how much to invest in each opportunity. Often how much to invest in each opportunity can be as important, or even more important, than what you invest in. There is a myriad of opinions and methods on this topic.
Some investment managers choose to avoid the problem altogether and simply allocate each of their positions equally. The investment management firm Walter Scott runs its portfolios this way, with funds being invested into 50 equal positions. By investing this way, Walter Scott ensures broad diversification. The portfolio manager will know that one mistake will not blow up their investment performance. There is a certain comfort in this, though it also ensures that one particularly good investment you make will not have a very big impact on your results either. It also means that your best idea and your 50th best idea will be worth the same in your results.
Other investment managers try to weight their portfolios according to an index or benchmark that they compete with. By doing so they reduce the risk of having drastically different performance than the benchmark they compete with. Unfortunately this also makes it extremely difficult for them to outperform that index as well.
I tend to believe in having a more concentrated approach to investing. Instead of having wide diversification I believe that you can enhance your performance while also reducing your risk by sticking to your best ideas and best investments. This can sometimes lead to more volatile portfolios, but overall I think it reduces the chances that you will experience a permanent loss of capital over time.
This approach is often followed by some of the world’s most successful investors like Warren Buffett, Charlie Munger, and George Soros. As Charlie Munger says
“The wise ones bet heavily when the world offers them the opportunity. They bet big when they have the odds. And the rest of the time, they don’t. It’s just that simple.”
This is consistent with my thinking on the subject. If you have taken the time to research 10-15 really great investments, and you know those investments in and out, including all of the potential risks and problems that could occur, then that is as sufficiently diversified as you need to be. Adding additional investments beyond that will probably only dilute your better ideas with worse ideas.
Assuming you’ve followed my line of thinking and you want to invest in a more concentrated manner, there is still the question of how much to allocate to each of your 10-15 best ideas. Many people just go on instinct and aren’t very scientific about how they allocate their funds. It certainly can be difficult to find the right balance between our investments, all of which will have their own merits and risks. Fortunately for us, very smart people have already done some work on this.
In 1956 a physicist at Bell Labs John Kelly spent time pondering this very question and published his findings under an article entitled “A New Interpretation of Information Rate”. His work and the formula it produced eventually came to be known as the Kelly Criterion. The Kelly Criterion became very popular among sports bettors as well as investors.
The Kelly Criterion is essentially this:
% of portfolio to invest = % advantage of investing / odds
In order to understand this better I think it’s good to do a simple example. Let’s say you are offered a coin toss where if you get heads you will be paid 2 times your bet, and if you get tails you will lose your bet. We know there is a 50% chance for either outcome so we have all of the inputs we need to use the Kelly Criterion. The formula looks like this:
% of portfolio to invest = (0.50) / 2
Our advantage is 0.5 because on a bet of $1 per coin toss we would win $2 if it comes up heads and we would lose $1 if it comes up tails. Therefore our expected profit is $0.50 ($2 x 50% chance of heads) - ($1 x 50% chance of tails). The odds are what we will win IF we win. In this case the win would be $2 on a $1 bet. Therefore if we solve for the Kelly Formula we should allocate 25% of our portfolio to this coin toss. (0.5/2 = 25%)
The Kelly Criterion works best when the odds of success are known. For example in casino games like Blackjack, it is possible to very accurately calculate your odds of winning based on what cards have been played from the deck. Mathematicians like Edward Thorp who wrote the book “Beat The Dealer”, were able to calculate that if certain cards had already been played from the deck, then the player might have a significant advantage over the dealer which could be quantified. Even if this advantage was only 1 or 2% (in other words, the odds of the player winning were 51% and the odds of the player losing were 49%), that advantage was enough to make a lot of money if the player could adjust his bet size accordingly to bet more when the odds were in the player’s favour. How much more? Well that’s where the Kelly Criterion comes into play.
If the player has a 2% advantage over the house on a particular hand and the odds they are getting are 1-1 (in blackjack of course the odds are actually a little better than 1-1 as a blackjack will pay 1.5-1 in most casinos.) then the player should risk up to 2% of their stack on each hand (2%/1 = 2%). Edward Thorp used this exact formula to successfully beat the casinos and make blackjack a profitable occupation.
Of course in the world of stock investing, the odds of success are not known and must be estimated, and the potential payoff is also not known. However these can be estimated conservatively and can still provide a useful indication of how much to invest. For example, if I do a valuation of the intrinsic value of a business and I determine its stock is trading at half of what I think is the intrinsic value I can then say that the potential return on my investment would be 100% if the stock eventually goes up to my intrinsic value. I can then estimate what the probability is of being right and having the stock reach my intrinsic value. This should be done conservatively as there are a lot of unknowns. But let’s say that I estimate my chances of success at 60%. Now I have all of the numbers I need to calculate my optimal investment according to the Kelly Criterion. The formula is:
% of portfolio to invest = (60% - 40%) / 100% = Invest 20% of your portfolio
This might be too aggressive for some people to invest 20% of their portfolio into a single investment but it is a way to maximize returns. For those who want to invest a little more conservatively you can always invest half of the recommended amount of the Kelly Criterion and it will still work.
This is more art than science but it can give you a good idea as to how much to invest. Using the formula can give you a higher limit on what you should be investing and then you can allocate what you will be comfortable with. For me the key idea behind the Kelly Criterion is that in order to maximize your returns, you need to be willing to bet heavily when the investment opportunity is really good. This is very contrary to more conventional advice about wide diversification and equating risk with volatility. We can see from famous investors like Warren Buffett, Charlie Munger, George Soros, and Bill Gross that investors who use the Kelly Criterion can be very successful.
- Craig White, BA, LL.B., CIM®
Craig White is an Investment Advisor at Endeavour Wealth Management with Industrial Alliance Securities Inc, an award-winning office as recognized by the Carson Group. Together with his partners he provides comprehensive wealth management planning for business owners, professionals and individual families.
This information has been prepared by Craig White an Investment Advisor for Industrial Alliance Securities Inc. (iA Securities) and does not necessarily reflect the opinion of iA Securities. The information contained in this newsletter comes from sources we believe reliable, but we cannot guarantee its accuracy or reliability. The opinions expressed are based on an analysis and interpretation dating from the date of publication and are subject to change without notice. Furthermore, they do not constitute an offer or solicitation to buy or sell any of the securities mentioned. The information contained herein may not apply to all types of investors. The Investment Advisor can open accounts only in the provinces in which they are registered.