How should I weight the stocks in my portfolio?
Investors spend most of their time analysing stocks to add to their portfolio. It makes sense. If an investor owns too many poor-quality stocks whose prices continually decline, they will never generate acceptable returns, no matter how good they are at portfolio management. However, the average investor often focuses too much on stock-picking and neglects to consider other aspects that are the key to outperformance. Perhaps the biggest one is how to weight the stocks that they pick.
This challenge doesn’t just impact individual investors. Bill Miller is often considered one of the greatest stock-pickers around. The fund he ran, Legg Mason Capital Management Value Trust, beat the S&P 500 index, after fees, for 15 consecutive years from 1991 through 2005. However, subsequent to 2006 he lost his investors all the previous cumulative outperformance. His downfall was being overweight companies whose performance was highly correlated to each other, such as American International Group, Wachovia, Washington Mutual, Freddie Mac, Countrywide Financial and Citigroup. Given that these companies were highly leveraged to the US property market, Miller’s losses in the Great Financial Crisis could have been much worse if governments and central banks hadn’t intervened.
The academic solution
That the correlation between stocks matters shouldn’t have surprised Miller. This concept has been the cornerstone of the academic approach to portfolio construction since the 1950s known as Modern Portfolio Theory (MPT). In 1952, Harry Markowitz wrote a paper called Portfolio Selection that defined what the optimal portfolio should be for any given set of assets. The theory applies equally to asset classes or the constituents of those, such as individual stocks. It was based on the rational assumption that investors would want to maximise their portfolio’s volatility-adjusted return. While volatility shouldn’t be the only consideration for investors, this assumption makes sense. If an investor could get the same return but a lower volatility, they could, in theory, use leverage to create an even higher return for the same volatility. Markowitz called the points where an investor can no longer generate higher returns without bearing more risk The Efficient Frontier.
To calculate the optimal portfolio, the investor needs to know the expected return of each asset and the covariance, the amount of each asset’s price that moves relative to the other assets. When Markowitz created this theory in 1952, it was impossible to calculate the efficient frontier for any real number of assets due to the complexity of the mathematics involved. So, the next step for many academics was to introduce the concept of market efficiency. This takes various forms, but the heart of the idea is that the market price includes all information and, therefore, cannot be beaten without bearing more risk. Under this assumption, the market portfolio of all investable assets can be shown to be on the efficient frontier. The conclusion is that investors should simply own the whole market via index trackers.
An investor who chooses their own stocks is unlikely to be an adherent to the stronger forms of the Efficient Market Hypothesis. Instead, they will want to apply MPT to weight stocks in their portfolio. And they can. The computing power available today enables any investor to calculate the efficient frontier for their portfolio, assuming they know each stock’s expected return and covariance. But here lies the issue. Investors who want to apply this theory often tend to take the historical values from the recent past as their estimates of these figures. The problem is that the actual values of these factors are unknowable: investors need to know the future values, not the past. Suppose they are optimising a portfolio comprising a stock market index and a bond market index. In that case, it may be reasonable to assume values related to the historical averages of these asset classes over the very long term. Even then, the correlation between major asset classes can change significantly over time and different economic conditions. For individual stocks, the volatility and covariance are unlikely to be stable over even short periods. As the saying goes, in theory, there is no difference between theory and practice - in practice, there is.
Market-capitalisation-weighting
As MPT can point towards owning an index tracker for those who don’t have an investing edge, it is worth considering if the structure of these is worth emulating. Most indexes are constructed using a market capitalisation weighting. The big advantage of a market-capitalisation-weighted portfolio is that it doesn’t require rebalancing. Since the increase in the price of any asset within the portfolio increases its desired weighting and actual weighting equally, no action is required to maintain the weighting. Not having to trade to retain the desired weighting means that costs should be very low, and high costs are one of the big reasons that investors underperform the market.
There are, however, a couple of reasons why market capitalisation weighting is not ideal. The first is that, by definition, a market-capitalisation-weighted index over-weights overvalued stocks and under-weights undervalued stocks. If a company is fundamentally overvalued, its price will be higher than its true value. Since market capitalisation is a function of price, a higher price means its weighting is higher in the index. Conversely, if a company is fundamentally undervalued, its price will be lower than its true value, which means its weighting is lower in the index.
The other concern with market-capitalisation weighting is that the largest companies in any index usually underperform, but this is where the index has the highest weighting. In a 2012 study called Too Big to Succeed, Rob Arnott found that investing in the largest company in each market sector was a terrible strategy. Two-thirds of such companies underperformed their sector over the next ten years. The average return from investing in the largest companies in each sector would have been 4.30% a year, less than the sector’s average over those ten years.
Whilst index tracker investors accept these concerns with market-capitalisation-weighting in return for low cost and ease of execution, it seems unlikely that a stock picker would want to base their strategy on market capitalisation given these drawbacks.
Equal-weighting
With an equal-weight portfolio, investors own the same amount in each pick. Quant strategies such as high StockRank investing tend to use this method. The reason is that an investor knows these stocks meet a set of criteria that should lead to outperformance, but they cannot further separate them. For example, there is evidence that companies with a StockRank of 90 or above outperform companies with a lower StockRank than this over the long term. However, there is no evidence that companies with a StockRank of 99 outperform those with a StockRank of 98. Hence, an investor would choose to own all SuperStocks equally (or a randomly sampled set of them).
Equal weighting is an excellent option for simple strategies. However, if an investor can tilt their portfolio weighting towards stocks that are more likely to generate higher or less correlated returns, this would add significant value.
Portfolio weighting criteria
Thankfully, there is a theory that can be of practical use to stock-pickers when weighting stocks in their portfolios. It is called the Kelly Criterion and was developed by John L. Kelly Jr. as part of his research into the mathematics of betting games. The Kelly Criterion says that in a series of bets you will always end up with the highest return by betting the proportion of your bankroll in proportion to your edge versus the odds you are offered. The Kelly Criterion became well known when it was used by the legendary mathematician, physicist and investor Edward O. Thorp to size bets while using the card counting systems for Blackjack that he developed in Las Vegas casinos. Thorp published a best-selling book called Beat the Dealer, which popularised his methods.
Using the Kelly Criterion sounds complex and runs into some of the same challenges as applying Markowitz’s Modern Portfolio Theory: an investor needs to know their edge and odds to calculate the proportion of their portfolio to invest. On top of this, they need to adapt the theory to multiple simultaneous opportunities rather than a series of consecutive bets. However, unlike MPT, investors can apply the principles of Kelly without having to apply the maths. The three principles are upside, certainty, and risk. Let’s go through each one.
Upside
The Kelly Criterion suggests that investors should increase their portfolio weighting when an investment has a higher upside. This sounds intuitively obvious. However, it bears making a conscious effort to estimate this compared to other portfolio investments. For example, stocks with large addressable markets or significant operational leverage may have greater potential for outsized returns. Conversely, low-growth stocks are unlikely to see a significant multiple expansion.
Certainty
Investors should hold more of stocks where they are more certain of a positive outcome. Some stocks have more predictable futures. They may have the protection of being in a regulated industry or have a significant proportion of their revenue secured via long-term contracts. In contrast, some stocks have more significant near-term uncertainty. There is a reason that investors dislike an unusual second-half weighting for a business. This is often a sign of short-term problems in demand for a company’s products. Not every company who hopes that they will turn it around in the second half does so. An investor’s portfolio holding should reflect that reality.
Risk
As risk increases, position size should decrease. Although volatility of share prices may be a risk factor for investors, it is by no means the only factor to consider. Here are some of the risks that investors will want to take into account:
Financing Risk - Companies with high levels of debt or weak balance sheets will be less able to weather a period of poor trading.
Management Risk - Management with a history of poor capital allocation, excessive remuneration, or being overly promotional will add an additional risk factor.
Product Risk - Companies with few products or that only serve one market are more exposed to the performance of that product or market.
Liquidity Risk – This is the risk of being unable to sell near the published market price when you want to. It usually makes smaller companies riskier.
Commodity Risk - Companies without a sustainable competitive advantage to control pricing are more likely to be exposed to commodity pricing, economic growth, inflation or obsolescence factors.
Correlation Risk – I don’t mean the mathematical covariance of stock prices but the common exposure they have to economic factors that are out of your control. A portfolio of companies in the same industry is undoubtedly risky, even if it is highly diversified.
Regulatory Risk - The risk is that changes in government or public opinion will cause the regulations to change to the detriment of the company.
Country or Political Risk - The quality of protections for companies or investors varies significantly worldwide. As does the risk of civil unrest, asset forfeiture or corruption. All of these may negatively impact an investment outcome.
Putting these together
When investors consider these factors together, their largest holdings should be those with the greatest upside, the most certainty of a positive outcome, and the lowest risk. One of the challenges is that these opportunities are relatively rare. This is why investors should be happy to own riskier stocks or those with more uncertain outcomes as long as the upside is still significant. However, they should do so with a smaller position size. One of the biggest mistakes investors tend to make is over-weighting very high-risk stocks because they have significant upside.
Likewise, it would be logical for an investor to own stocks where the upside returns are positive but not phenomenal, as long as these are lower risk or have a higher certainty of a positive outcome. Again, a typical investment mistake is to ignore boring stocks that are somewhat undervalued in the search for multi-baggers. Only pursuing very high return stocks may sound like a great idea, but the reality is that these are very hard to spot ahead of time.
Conversely, investors shouldn’t own uncertain, high-risk socks if they have the potential for only low returns. When investors generate significant returns in a particular stock, they may have a large position size, even if the risk has increased and the undervaluation has disappeared. While it can be important to run winners, it is worth bearing in mind that for hedge funds, their largest positions usually underperform the rest of their portfolio. These tend to get to number one by generating high returns in the past rather than having the potential of being a high-return stock in the future.
A final caution
One of the things that mathematical studies of the Kelly Criterion have shown is the consequence of overbetting. That is, increasing bet size beyond the level the theory suggests. The outcome is always a significant loss of capital. In most cases, it is at a level that would become unrecoverable for most investors. The key that betting practitioners have found is to reduce their betting sizes to half or lower than the Kelly Criterion suggests. The drop in returns is not significant and avoids the problem of minor uncertainties in odds or edge leading to wipeouts. Investors should learn from this and exercise caution in position-sizing, even when they believe they have found high upside, high certainty and low-risk stocks.
When weighting stocks in an investor’s portfolio, it pays to be approximately right rather than precisely wrong. Different investors will have different assessments of the potential and risks of different stocks. However, the skills required to be a good stock picker are the same as those required to assess upside, certainty, and risk. Hence, any investor with skill in stock picking can also be great at portfolio management. They simply have to apply these skills in a consistent way.