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 July 2002 Think Inside the Box Introducing Portfolio 5: A New Quantitative Portfolio
For equities, Morningstar's "stylebox" has always done a good job of capturing these distinctions. In fact, the stylebox is arguably Morningstar's greatest contribution to the investing public. As you probably already know, the stylebox divides the domestic equity market into nine different sections based on capitalization (large, mid, and small cap) and style (value, growth, and blend). It's a simple 3x3 grid with the styles heading the columns and capitalizations on each row.
Funds, based on their underlying stocks, are divided into these nine different categories. Morningstar recently altered the way they assign style labels, but the idea is pretty straightforward: Funds that hold stocks with growth characteristics above those of the comparable market benchmark (e.g. P/E) are considered to be "growth" while those with falling below the market average are "value". Those near the market are "blends". Barra applies a similar procedure in dividing stocks of the S&P large, mid, and small cap indexes. The Frank Russell Company does the same thing with their equity indexes. Investors combine stocks, funds and managers from different categories in an effort to diversify their portfolios. Since different styles and capitalizations go in and out of favor, a mix of them should add stability in a turbulent market. Stocks in a BoxAccording to Modern Portfolio Theory, this is a sound approach, so why guess at it? We thought we'd test it out by adding a little quantitative structure to the allocation process. Not only did the results shed some light on the effectiveness of the approach, they also yielded some surprising conclusions about recent equity performance.
We focused on the S&P style indexes rather than the Russells because the latter are only reconstituted once a year at the end of June. The further you get away from that date, the fewer stocks they hold due to mergers, acquisitions, and bankruptcies. Market movements can also make value stocks out of growth stocks and vice versa. The S&P indexes get additions and deletions as necessary. They always hold the number of stocks implied by their name and stocks move from one index to another as necessary throughout the year. That seemed more appropriate for our purposes. In addition to the S&P 500 large-cap index, the S&P 400 is a mid-cap index and the S&P 600 is a small-cap index. Each has a corresponding S&P/Barra index for value and growth which allowed us to fill in all nine positions in the stylebox. Next we took these nine different series and backtested them using the Ibbotson historical database and optimizer. The common start date for all nine series is January 1, 1994, so we used March 31, 1995 as our beginning date. That provided over 1-year's worth of data while giving us 7 years (through March 31, 2002) to examine, long enough to provide meaningful results. We assumed the "Stylebox Portfolio" would be reformulated every three months. New portfolios would go into effect at the beginning of each calendar quarter. No rebalancing would occur in the intervening months. To keep the backtest as accurate as possible, we used strictly historical data, adding the new three months each time we reformulated the portfolio. Accordingly, our first portfolio for the 2nd quarter of 1995 was based on the indexes' returns in the preceding 15 months. We added the results from the 2nd quarter to create the model for the 3rd quarter, etc. We ran the data through the Ibbotson optimization software to create an efficient frontier. This, according to Modern Portfolio Theory, represents the range of efficient mixes of our index inputs. In this context, the most
This presented a problem we hadn't anticipated: How do you create the frontier? There are three viable ways to do this, so we tested them all. The first approach is to use strictly historical data. The underlying assumption is that the future will be like the past. That's a fine approach of you have a lot of data points, but in this case we only had a little over eight years worth. Potentially skewing it was the fact that growth stocks dominated in 6 of the 8 years. As you'd expect, this approach produced the poorest results. The second approach ties historical data to current economic and financial conditions. The latter are modeled through risk premiums. For example, this so-called "building block" method starts with the current risk-free rate (usually that of a short-term T-Bill) and adds to it the current equity risk premium and for small or mid-cap stocks, a small stock risk premium. The main drawback to using the building block approach was that we were asking it to do something it was not designed to do. Roger Ibbotson created it for use with series of different capitalizations, not styles. As a result, it yields the same return projections for each index as well as its growth and value variants. The only thing that differs is the risk. As you'll notice from some of the upcoming charts, style indexes of the same capitalization produce vastly different returns. Because of this, we moved on to the third method.
This approach is the Capital Asset Pricing Model. The Ibbotson software uses a longer historical period to calculate the "market" return. It then uses regression analysis over the backtest period to generate alphas and betas for each of our 9 inputs. Based on the calculated market return and current risk-free rate, it then projects the expected return for each of the 9 inputs and creates the efficient frontier for the coming quarter. This was the method we ultimately adopted. Problems Picking PointsBut once we knew how to create the efficient frontier, we ran into the second problem: Which portfolio should we use for our model? In other words, where should the Stylebox Portfolio fall along the frontier? Since all are efficient, it really boils down to a question of risk. Rather than just arbitrarily pick a point, we tried four different reasonable approaches. Each is illustrated on Chart 1. The "Maximum Sharpe Ratio" marks the point on the frontier with the highest risk-adjusted return. Without going into great detail, the Sharpe Ratio is a way to measure how much return you receive for each additional increment of risk. Risk is defined as standard deviation and is measured along the horizontal axis. Annual return is measured on the vertical axis. Just looking at the shape of the efficient frontier, the portfolio with the maximum Sharpe Ratio will always fall at the inflection point where the frontier begins to level off. Why? Because to the right of that point the additional return (increases along the vertical axis) diminishes for each additional increment of risk (movement along the horizontal axis). In each instance, this inflection point lands on the left half of the frontier, so the Maximum Sharpe Ratio Portfolio tends to offer modest returns. The second approach was to seek the highest return. This is the portfolio falling at the right end of the frontier. Interestingly, this point was always anchored by one of the specific input series, so this portfolio was never diversified, always investing 100% in that particular index. It also always had the highest risk of any alternative.
The third approach was a compromise between the first two. We wanted to find a point along the efficient frontier that provided a risk-adjusted return greater than that of the Maximum Sharpe Ratio but with more diversification and less risk than the Maximum Return Portfolio. Given that the area between the first two points was roughly the last two-thirds of the efficient frontier, we tested two other points, one in the middle of the frontier (the "Frontier Midpoint Portfolio") and the other three-quarters of the way along the frontier (the "Point 75 Portfolio"). Throughout the test period, neither held less than two series and occasionally as many as four. Results were below the maximum, but risk was lower, too. The ResultsCharts 2 and 3 show the results of the backtest. The first shows cumulative returns over the seven-year period from April 1, 1995 through March 31, 2002. Although many investors follow the S&P 500, the most appropriate benchmark for the broad market is the combination of the S&P large, mid, and small cap indexes: the S&P 1500 Super Composite. Despite large cap growth's remarkable run in the late-90s, mid cap growth was the place to be. As Chart 2 clearly demonstrates, not only was this style in the lead at the end of the seven years, it was at the forefront throughout the test. Perhaps more surprising was the fact that the Maximum Sharpe Ratio Portfolio never used this series at any time in the backtest. All other portfolios made extensive use of mid cap growth beginning in 1997.
For the tested portfolios, cumulative results are about what you'd expect. Maximum Sharpe Ratio had the lowest return while the Maximum Return Portfolio lived up to its name. The Point 75 Portfolio was rewarded for its additional risk with a higher return than that of the Point 50 Portfolio. As Chart 3 illustrates, this order is also maintained in the 1, 3, 5, and 7-year returns. Again there's a surprise from the indexes -- small and mid caps did well across the entire seven-year backtest. While they were the clear winners in the past one and three years, they also hung with large caps over the five and seven-year periods as well. You won't find a better argument for diversification. As far as the tested mixes, we'd go with the Point 75 Portfolio. As Charts 2 and 3 show, its cumulative results are in line with those of the S&P 1500. Throughout the test period, it offered more diversification than the Maximum Return Portfolio, while outperforming the other two alternatives.
The ultimate goal was to come up with a model that the average investor could use. While it isn't possible to go out and buy a large cap growth index, you can purchase vehicles that closely track them. Various "iShares Trusts" advised by Barclays Global Fund Advisors, closely track a wide range of indexes. Called "exchange traded funds" or ETFs, they are listed on the American Stock Exchange. Unlike traditional open-end mutual funds, they can be traded any time during regular market hours and may carry a premium or discount to the underlying index. According to the prospectus, the advisor expects the correlation between the trusts (before fees and expenses) and the index to be 95% or greater. Also traded on the American Exchange are S&P Depository Receipts, better known as SPDRs. While they don't cover as many indexes as the iShares, SPDRs trade higher volumes and have smaller spreads. Based on the latter characteristic, they are more efficient trading vehicles. Given the availability and liquidity of these vehicles, it is possible for the average investor to not only allocate his or her portfolio across styles and capitalizations, it's possible to trade it as well. By only using a handful of ETFs, holdings can easily be adapted to changing market conditions.
Chart 4 shows how our ETF model has performed this year. So far it's tracked amazingly closely with the S&P 1500. Keep in mind this portfolio will never have more than nine holdings and so far this year has only had two. It's not unlike an index mutual fund, but without the surprise year-end capital gains. We'll be reallocating the Stylebox Portfolio every three months, usually around the second week of each quarter. Its performance going back to January 1, 2002 will be tracked weekly on the Home Page as "Portfolio 5". Starting in September, Historical Performance will include commentary on its performance and current composition. Morningstar's ratings may come and go, but the stylebox endures. Hopefully this will also hold true for the Stylebox Portfolio. Search this site! Just enter you key word or words:
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FFECTIVE THIS MONTH, MUTUAL FUND INVESTORS are adjusting to the new system of assigning "star" ratings at Morningstar. The firm believes this change is necessary since most funds no longer have a broad-based equity or fixed income focus. Instead, the majority specialize in specific capitalizations and/or styles.
