Market Timing Approaches

            There as probably as many market timing approaches as there are investors. Some of these approaches are based upon non-financial indicators, some on macroeconomic variables such as interest rates and business cycles and some draw on the valuation tools that we used to analyze individual stocks – discounted cashflow and relative valuation models.

Market Timing based upon Non-financial Indicators

            Through the decades, there are some investors who have claimed to foretell the market’s future by looking at non-financial indicators. Some of these indicators, such as whether the NFC or AFC team wins the Super Bowl are clearly of dubious origin and would fall into a category that we title spurious indicators. Other indicators such as the hemline index, which relates stock prices to the length of hemlines on skirts, fall into the grouping of “feel good indicators” that measure the overall mood of people in the economy, who after all are both the consumers who act as the engine for the economy and as investors determining prices. Finally, there are the “hype indicators” that measure whether market prices are becoming disconnected from reality.

Spurious Indicators

Millions of investors track what happens to their stocks and to the market every day and it is not surprising that they find other occurrences that seem to predict what the market will do next year. Consider one very widely talked-about indicator – who wins the Super Bowl.[1] In the 35 years that the Super Bowl has been played from 1966 to 2001, the winner has come from the National Football Conference (or is an old pre-merger NFL team like the Steelers or Colts) 25 years, and the market has risen in 22 out of the 25 years. In the 10 years that an American Football Conference team has won, the market has fallen 7 times. In fact, there are academic researchers who claim that the success rate of 83% (29 out of 35 years) is far too high to due to chance. [2]

So why not invest in the market after observing who wins the Super Bowl? There are several potential problems. First, we disagree that chance cannot explain this phenomenon. When you have hundreds of potential indicators that you can use to time markets, there will be some that show an unusually high correlation purely by chance. Second, a forecast of market direction (up or down) does not really qualify as market timing, since how much the market goes up clearly does make a difference. Third, you should always be cautious when you can find no economic link between the indicator and the market. There is no conceivable reason who wins the Super Bowl should affect or be correlated with overall economic performance. Indicators such as these may make for amusing anecdotes at parties but can be lethal to your portfolio as market timing devices.

Feel Good Indicators

            When people feel optimistic about the future, it is not just stock prices that are affected by this optimism. Often, there are social consequences as well, with styles and social mores affected by the fact that investors and consumers feel good about the economy. In the 1920s, for instance, you had the Great Gatsby and the go-go years, as people partied and the markets zoomed up. In the 1980s, in another big bull market, you had the storied parties and excesses of Wall Street, documented in books like Liars Poker and movies like Wall Street. It is not surprising, therefore, that people have discovered linkages between social indicators and Wall Street. Consider, for instance, an index that has been around for decades called the hemline index that finds a correlation between the hemlines on women’s skirts and the stock market. This politically incorrect index is based on the notion that shorter dresses and shirts are associated with rising stock prices whereas longer dresses are predictors of stock market decline. Assuming the index works, we would argue that you are seeing a manifestation of the same phenomenon. As people get more upbeat, fashions do seem to get more daring (with higher hemlines following) and markets also seem to go up. You could undoubtedly construct other indices that have similar correlations. For instance, you should expect to see a high correlation between demand at highly priced restaurants at New York City (or wherever young investment bankers and traders go) and the market.

            The problem with feel good indicators, in general, is that they tend to be contemporaneous or lagging rather than leading indicators. In other words, the hemlines don’t drop before the markets drop but in conjunction with or after a market drop. As an investor, these indicators are off little use, since your objective is to get out before the market drops and to get in before the market goes up.

Hype Indicators

            It is said that Joseph Kennedy, a well known speculator on stocks in his own time, knew it was time to get out of the market when he heard his shoe-shine boy talking about stocks. In our own time, there are some who believe that the market peaked when financial channel CNBC’s ratings exceeded those of long-running soap operas. In fact, one recent indicator called the “cocktail party chatter” indicator tracks three measures – the time elapsed at a party before talk turns to stocks, the average age of the people discussing stocks and the fad component of the chatter. According to the indicator, the less time it takes for the talk to turn to stocks, the lower the average age of the market discussants and the greater the fad component, the more negative you should be about future stock price movements.

Harking back to our discussion of bubbles, remember that propagation is critical to bubbles getting bigger. In our media world, this will involve print, television and the internet and an overflow into day-to-day conversations. Thus, the discussion at the water cooler in a typical business is more likely to be about stocks than about football or other such daily (and more normal) obsessions, when markets are buoyant.

While hype indicators, of all non-financial indicators, offer the most promise as predictors of the market, they do suffer from several limitations. For instance, defining what constitutes abnormal can be tricky in a world where standards and tastes are shifting – a high rating for CNBC may be indicate too much hype or may be just reflecting of the fact that viewers find financial markets to be both more entertaining and less predictable than a typical soap opera. Even if we decide that there is an abnormally high interest in the market today and you conclude (based upon the hype indicators) that stocks are over valued, there is no guarantee that stocks will not get more overvalued, before the correction occurs. In other words, hype indicators may tell you that a market is overvalued, but they don’t tell you when the correction will occur.

Market Timing based upon Technical Indicators

            In chapter 7, we examined a number of chart patterns and technical indicators used by analysts to differentiate between under and over valued stocks. Many of these indicators are also used by analysts to determine whether and by how much the entire market is under or over valued. In this section, we consider some of these indicators.

Past Prices

            In chapter 7, we looked at evidence of negative long term correlation in stock prices – stocks that have gone up the most in recent periods (defined as semi-annual or annual ) are more likely to go down in future periods. Studies do not seem to find similar evidence when it comes to the overall market. If markets have gone up significantly in the most recent years, there is no evidence that market returns in future years will be negative. If we consolidate stock returns from 1871 to 2001, into five-year periods, we find a positive correlation of 20.85% between five-year period returns – in other words, positive returns over the last five years are more likely to be followed by positive returns than negative returns in the next 5 years. In table 12.1, we report on the probabilities of an up-year and a down-year following a series of scenarios, ranging from 2 down years in a row to 2 up years in a row, based upon actual stock price data from 1871 to 2001.

Table 12.1:Market Performance

Priors

Number of occurrences

% of positive returns

Average return

After two down years

19

57.90%

2.95%

After one down year

30

60.00%

7.76%

After one up year

30

83.33%

10.92%

After two up years

51

50.98%

2.79%

It is true that markets are more likely to go down after two years of positive performance than under any other scenario, but there is also evidence of price momentum, with the odds of an up year increasing if the previous year was an up year. Does this mean that we should sell all our stocks after two good years? We don’t think so, for two reasons.  First, the probabilities of up and down years do change but note that the likelihood of another good year remains more than 50% even after 2 consecutive good years in the market. Thus, the cost of being out of the market is substantial with this market timing strategy. Second, the fact that the market is overpriced does not mean that all stocks are over priced. As a stock picker, you may be able to find under valued stocks even in an over priced market.

            Another price-based indicator that receives attention at least from the media at the beginning of each calendar year is the January indicator. The indicator posits that as January goes, so goes the year – if stocks are up, the market will be up for the year, but a bad beginning usually precedes a poor year.[3] According to the venerable Stock Trader’s Almanac that is compiled every year by Yale Hirsch, this indicator has worked 88% of the time. Note, though that if you exclude January from the year’s returns and compute the returns over the remaining 11 months of the year, the signal becomes much weaker and returns are negative only 50% of the time. Thus, selling your stocks after stocks have gone down in January may not protect you from poor returns.

Trading Volume

            There are some analysts who believe that trading volume can be a much better indicator of future market returns than past prices. In fact, there are a number of technical indicators that are used to forecast changes in market director. Volume indicators are widely used to forecast future market movements. In fact, price increases that occur without much trading volume are viewed as less likely to carry over into the next trading period than those that are accompanied by heavy volume. At the same time, very heavy volume can also indicate turning points in markets. For instance, a drop in the index with very heavy trading volume is called a selling climax and may be viewed as a sign that the market has hit bottom. This supposedly removes most of the bearish investors from the mix, opening the market up presumably to more optimistic investors. On the other hand, an increase in the index accompanied by heavy trading volume may be viewed as a sign that market has topped out. Another widely used indicator looks at the trading volume on puts as a ratio of the trading volume on calls. This ratio, which is called the put-call ratio is often used as a contrarian indicator. When investors become more bearish, they sell more puts and this (as the contrarian argument goes) is a good sign for the future of the market.

            Technical analysts also use money flow, which is the difference between uptick volume and downtick volume, as predictor of market movements. An increase in the money tick is viewed as a positive signal for future market movements whereas a decrease is viewed as a bearish signal. Using daily money flows from July 1997 to June 1998, Bennett and Sias find that money flow is highly correlated with returns in the same period, which is not surprising. While they find no predictive ability with short period returns – five day returns are not correlated with money flow in the previous five days – they do find some predictive ability for longer periods. With 40-day returns and money flow over the prior 40 days, for instance, there is a link between high money flow and positive stock returns.

            Chan, Hameed and Tong extend this analysis to global equity markets. They find that equity markets show momentum – markets that have done well in the recent past are more likely to continue doing well,, whereas markets that have done badly remain poor performers. However, they find that the momentum effect is stronger for equity markets that have high trading volume and weaker in markets with low trading volume.

Volatility

            In recent years, a number of studies have uncovered a relationship between changes in market volatility and future returns. One study by Haugen, Talmor and Torous in 1991 found that increases in market volatility cause an immediate drop in stock prices but that stock returns increase in subsequent periods. They looked at daily price volatility from 1897 through 1988 and look for time periods where the volatility has increased or decreased significantly, relative to prior periods. [4] They then look at returns both at the time of the volatility change and in the weeks following for both volatility increases and decreases, and their results are summarized in Figure 12.1:

Note that volatility increases cause stock prices to drop but that stock prices increase in the following four weeks. With volatility decreases, stock prices increase at the time of the volatility change, and they continue to increase in the weeks after, albeit at a slower pace.

            Does this mean that you should buy stocks after an increase in volatility?  Not necessarily. The increase in returns in the weeks following a volatility increase may just reflect the reality that stocks are riskier. However, if you believe that a surge in volatility is temporary and that stock volatility will revert back to normal levels, a strategy of buying stocks after an increase in equity market volatility may bear fruit.

Other Technical Indicators

            There are a number of non-price indicators that are used by analysts to forecast future market movements. As with stock-specific technical indicators, market-wide indicators are often used in contradictory ways by momentum and contrarian analysts, with an increase in a specific indicator being viewed as bullish by one group and bearish by the other. Since we did cover technical indicators in depth in chapter 7, we will make only a short mention of some of these indicators in this section, categorized into price and sentiment indicators:

While many of these indicators are used widely, they are mostly backed with anecdotal rather than empirical evidence.

Market Timing based upon Normal Ranges (Mean Reversion)

            There are many investors who believe that prices tend to revert back to what can be called normal levels after extended periods where they might deviate from these norms. With the equity market, the normal range is defined usually in terms of PE ratios whereas with the bond market, a normal range of interest rates is used to justify betting on market direction.

Is there a normal range for PE ratios?

            Buy if the PE drops below 12 and sell if it rises above 18. You will see variations of this advice in many market testing newsletters. The implicit belief here is that there is a normal range for PE ratio and that if the PE rises above the top end of the range, stocks are likely to be overvalued, whereas if they fall below the bottom of the range, they are likely to be overvalued. While the approach is straightforward, where does the normal range of PE ratios come from? In most cases, it seems to come from looking at history and attaching a subjective judgment on the upper and lower limits.

            Consider, for instance, figure 12.2 which presents PE ratios for the S&P 500 going back to 1960.

We have attempted to draw a normal range for interest rates in the United States, based upon history, though it indicates the subjective judgments that we had to make along the way. Based upon our band, stocks would be considered as overvalued if they traded at a PE ratio greater than 22 or less than 12.

            The limitations of this approach should be obvious. In addition to trusting history to repeat itself, we are making two other assumptions. The first is that we can identify a normal trading range by looking at historical data. As you can see from the graph, you will not get any consensus – someone else looking at this graph might end up with a different band for PE. The second is that the fundamentals have not shifted significantly over time. If interest rates are much lower today than they have been historically, you would expect stocks to trade at much higher PE ratios than they have historically. How much higher? We will look at this question in more detail in the later parts of this chapter.

Normal Range of Interest Rates

            Some analysts hypothesize that market interest rates move within a normal range. Under this hypothesis, when interest rates approach the high end of the range, they are more likely to decrease, and when they approach the low end of the range, they are more likely to increase.  This hypothesis is corroborated by two pieces of evidence:

1. Slope of the Yield Curve: The yield curve, which reflects future expectations about interest rates, is more likely to be downward sloping when interest rates are high than when there are low. Thus, investors are more likely to expect interest rates to come down if they are high now and go up, if they are low now. Table 12.2 below summarizes the frequency of downward sloping yield curves as a function of the level of interest rates.[7]

Table 12.2: Yield Curves and the Level of Interest Rates

                        1-year Corporate Bond Rate                   Slope of Yield Curve

                                                                        Positive            Flat                  Negative

                        Above 4.40%                           0                      0                      20

      1900-70     3.25% - 4.40%                        10                    10                    5

                        Below 3.25%                           26                    0                      0

      1971-2000 Above 8.00%                           4                      1                      3

                        Below 8.00%                           15                    6                      1

      This evidence is consistent with the hypothesis that maintains interest rates move within a normal range; when they approach the upper end (lower end) of the normal range, the yield curve is more likely to be downward sloping (upward sloping).        

2. Interest rate level and expected change: More significantly, investors’ expectations about future interest rate movements seem to be borne out by actual changes in interest rates. When changes in interest rates are regressed against the current level of interest rates, there is a negative and significant relationship between the level of the rates and the change in rates in subsequent periods, i.e., there is a much greater likelihood of a drop in interest rates next period if interest rates are high in this one, and a much greater chance of rates increasing in future periods if interest rates are low in this one. For instance, using treasury bond rates from 1970 to 1995 and regressing the change in interest rates (D Interest Ratet) in each year against the level of rates at the end of the prior year (Interest Ratet-1), we arrive at the following results:

D Interest Ratet = 0.0139 - 0.1456 Interest Ratet-1       R2=.0728

                                                   (1.29)       (1.81)

This regression suggests two things. One is that the change in interest rates in this period is negatively correlated with the level of rates at the end of the prior year; if rates were high (low), they were more likely to decrease (increase). Second, for every 1% increase in the level of current rates, the expected drop in interest rates in the next period increases by 0.1456%.

This evidence has to be considered with some caveats. The first is that the proportion of interest rate changes in future periods explained by the current level of rates is relatively small (about 7.28%); there are clearly a large number of other factors, most of which are unpredictable, that affect interest rate changes. The second is that the normal range of interest rates, which is based upon past experience, might shift if the underlying inflation changes dramatically as it did in the 1970s in the United States. Consequently, many firms that delayed borrowing in the early part of that decade, because they thought that interest rates were at the high end of the range, found themselves facing higher and higher rates in each of the following years.

Hindsight is 20/20

            Market timing always seems simple when you look back in time. After the fact, you can always find obvious signals of market reversals – bull markets turning to bear markets or vice versa. Thus, in 2001, there were investors who looked back at 1999 and bemoaned the fact that they missed getting out of stocks when the market topped at the end of that year. At that time, though, the signs were not so obvious. There were analysts who argued that the market was overvalued and indicators that supported that point of view, but there were just as many analysts, if not more, who saw the market continuing to book and had supporting models.

.In practice, there is never a consensus among investors on whether markets have hit bottom or peaked at the time that it occurs. It is an interesting fact that optimism about the future is greatest just as markets top out and the market mood is darkest just as markets turn around. To succeed at market timing, you cannot wait until a bottom has been established before buying or for a market top before selling. If you do, you will miss much of the subsequent payoff.

Market Timing based upon Fundamentals

            Just as the prices of individual stocks must reflect their cashflows, growth potential and risk, entire markets (equity, bond and real asset) have to reflect the fundamentals of these assets. If they do not, you can argue that they are misvalued. In this section, we consider two ways in which we can bring fundamentals into market timing models.  In the first, we try to develop market timing strategies based upon the level of fundaemental variables – interest rates and economic growth, for instance. In the second, we try to extend the valuation techniques developed for individual stocks to markets.

Fundamental Indicators

            You can try to time markets by developing simple signals based upon macro economic variables. In this section, we will consider some of these signals – some old and some new – that have been used by portfolio managers as market timing tools.

Short term Interest Rates

            Buy stocks when short-term rates (treasury bills) are low and sell them when short term rates are high, or so goes the conventional wisdom. But is there a basis to this advice? In table 12.3, we examine stock returns under four treasury bill scenarios – a decline in rates of more than 1% over the prior year, a drop of between 0 and 1%, an increase in rates of less than 1% and an increase of more than 1% between 1928 and 2001.

Table 12.3: Stock Returns and Treasury Bill Rates

 

 

In following year

Change in T.Bill rate

Number of years

% of up years

Average Annual returns

Drop by more than 1%

10

70%

10.58%

Drop between 0 and 1%

24

75%

13.17%

Increase between 0 and 1%

26

69.23%

11.94%

Incrase more than 1%

13

61.54%

8.90%

In this case, there is surprisingly strong empirical evidence backing up the proposition that a drop in the treasury bill rate seems to predict high stock market returns. Generally speaking, markets are more likely to go up in years after the treasury bill rate has decreased and earn higher returns for investors.[8]

This result has been confirmed by a number of academic studies. Ang and Baekart (2001) document that treasury bill rates dominate other variables as a predictor of short term stock market movements. Breen, Glosten and Jagannathan (1989) evaluate a strategy of switching from stock to cash and vice versa, depending upon the treasury bill rate and conclude that such a strategy would have added about 2% in excess returns to an actively managed portfolio.

            In a recent study that does raise cautionary notes about this strategy, Abhyankar and Davies (2002) examine the correlation between treasury bill rates and stock market returns in sub-periods from 1929 to 2000. They find that almost all of the predictability of stock market returns comes from the 1950-1975 time period, and that short term rates have had almost no predictive power since 1975. They also conclude that short rates have more predictive power with the durable goods sector and with smaller companies than they do with the entire market.

            In conclusion, then, you should be aware of short term rates when you invest in the market, but the value of short term rates as a predictor of stock market movements has decreased over the last few decades. Its remaining predictive power seems to be restricted to the short term and to sub-sectors of the market.

Treasury Bond Rate

            Intuitively, it is the treasury bond rate – the long-term riskless rate – that should have a much stronger impact on stock prices, since it offers a direct alternative to investing in stocks for the long term. If you can make 8% investing risklessly in treasuries for the next 30 years, why would you settle for less when investing in stocks? Thus, we should expect to see stock prices go up if the treasury bond rate comes down and go down, if the rate goes up. Figure 12.3 presents a scatter plot of returns on stock returns each year and the T.Bond rate at the end of the prior year:


In 1981, for instance, the treasury bond rate at the start of the year was 14% and the return on the stock index during the year was 15%. In 1961, the treasury bond rate was 2% and the return on stocks during the year was –11%. If there is a relationship between treasury bond rates and stock returns during the period, it is not strong enough to be obvious and there seems to be little support for the proposition that stock returns are high when interest rates are low and low when interest rates are high.  In fact, stocks did very well in 1980 and 1981, even though interest rates were very high at the beginning of both those years and very badly in 1961, notwithstanding the fact that the treasury bond rate was only 2% at the end of the prior year.

This link between treasury bond rates and stock returns should become even stronger if we consider how much we can earn as a return on stocks. You could define this return narrowly as the dividend yield (dividends/current stock prices) or use a much broader measure, such as earnings yield, which looks at the overall earnings on the market as a percent of the current level of the index. The earnings yield is the inverse of the price earnings ratio and is used widely by market strategists. Rather than focus on the level of the treasury bond rate, market strategists often look at the difference between earnings yields and the treasury bond rate. In simpler terms, they believe that it is best to invest in stocks when earnings yields are high, relative to the treasury bond rate. In fact, there are some strategists who believe that stocks are over valued when the earnings yield is lower than the treasury bond rate. To examine this proposition, we looked at the difference between the earnings yield and the T.Bond rate at the end of every year from 1960 to 2000 and the returns on the S&P 500 in the following year (see table 12.4)

Table 12.4: Earnings Yield, T.Bond Rates and Stock Returns: 1960 –2001

Earnings yield - T.Bond Rate

Number of years

Average

Standard Deviation

Maximum

Minimum

> 2%

8

11.33%

16.89%

31.55%

-11.81%

1 -2%

5

-0.38%

20.38%

18.89%

-29.72%

0-1%

2

19.71%

0.79%

20.26%

19.15%

-1-0%

6

11.21%

12.93%

27.25%

-11.36%

-2-1%

15

9.81%

17.33%

34.11%

-17.37%

< -2%

5

3.04%

8.40%

12.40%

-10.14%

The relationship is tenuous at best. When the earnings yield exceeds the treasury bond rate by more than 2%, which has occurred in 8 out of the 41 years, the return on the S& P 500 in the following year has averaged 11.33%. However, the returns are almost as good when the earnings yield has lagged the treasury bond rate by zero to 1%. It is true that the annual returns are only 3.04% in the five years following periods when the earnings yield was lower than the treasury bond rate by more than 2%, but the annual returns were also negative in the 5 years when the earnings yield exceeded the treasury bond rate by 1-2%.  Thus, there seems to be little historical support for using earnings yield and treasury bond rates to predict future stock market movements.

Business Cycles

            As with treasury bonds, there is an intuitive link between the level of stock prices and economic growth. You would expect stocks to do much better in economic booms than during recessions. What makes this relationship tricky, however, is that market movements are based upon predictions of changes in economic activity in the future, rather than levels of activity. In other words, you may see stock prices rising in the depths of a recession, if investors expect the economy to begin recovering in the next few months. Alternatively, you may see stock prices drop even in the midst of robust economic growth, if the growth does not measure up to expectations. In figure 12.4, we have graphed the S&P 500 index and GDP growth going back to 1960:

There is a positive relationship between GEP growth during a year and stock returns during the year, but there is also a lot of noise in the relationship. Even if the relationship were strong enough to pass muster, you cannot use it for market timing unless you can forecast real economic growth. The real question then becomes whether you can make forecasts of future stock market movements after observing economic growth in the last year. To examine whether there is any potential payoff to investing after observing economic growth in the prior year, we looked at the relationship between economic growth in a year and stock returns in the subsequent year, using data from 1929 to 2001 in table 12.5:

Table 12.5:Real Economic Growth as a predictor of Stock Returns: 1960 – 2001

 

 

Returns in Next Year

GDP Annual  Growth

Number of years

Average Return

Standard deviation in returns

Best Year

Worst Year

>5%

23

10.84%

21.37%

46.74%

-35.34%

3.5%-5%

22

14.60%

16.63%

52.56%

-11.85%

2-3.5%

6

12.37%

13.95%

26.64%

-8.81%

0-2%

5

19.43%

23.29%

43.72%

-10.46%

<0%

16

9.94%

22.68%

49.98%

-43.84%

All years

72

12.42%

19.50%

52.56%

-43.84%

 

There seems to be no clearly discernible relationship between returns next year and GDP growth this year. It is true that the years with negative GDP growth are followed by the lowest stock returns, but the average stock returns in this scenario are barely higher than the average returns you would have earned if you had bought after the best economic growth years (growth exceeds 5%).

            If you can forecast future growth in the economy, it can be useful at two levels. One is in overall market timing, since you will steer more of your funds into stocks prior to better-than-expected economic growth and away from stocks when you foresee the economy slowing. You can also use the information to over invest in those sectors that are most sensitive to the economic cycle – automobile and housing stocks, for instance – if you believe that robust economic growth is around the corner.

Intrinsic Value Models

            One way in which we can take the individual fundamentals that we considered in the last section and consolidate them into one market view is to do an intrinsic valuation of the entire market. What, you might ask, is an intrinsic valuation? Back in chapter 4, we consider how an individual stock can be valued using a discounted cash flow model as the present value of expected cashflows in the future. A market is composed of individual assets, and if individual assets can be valued using discounted cashflow models, we see no reason why the entire market cannot be valued as the present value of expected cashflows. In this section, we consider how best to extend discounted cashflow models to valuing the market, and the value that may be added from doing so.

Extending DCF Models to the Market

            Consider, for instance, the dividend discount model that we introduced in chapter 4. We argued that the value of a stock can be written as the present value of the expected dividends from owning the stock, discounted back at the cost of equity.  Extending this argument to an index, the value of an index can also be written as the present value of the expected dividends on the index. Thus, if the dividends on the entire stock index are expected to be $ 40 next year, the expected growth rate in perpetuity is expected to be 4% and the cost of equity for the average risk stock is expected to be 9%, you could value the index as follows:

Value of index = Expected dividends next year / (Cost of equity – Expected growth rate)

                        = 40 / (.09 - .04) = 800

As with an individual stock, this model can be extended to allow for high growth. Thus, if you expected dividends to grow 10% a year for the next 5 years and then expect the growth rate to drop to 4% in perpetuity, the value of the index can be computed in Table 12.6.

Table 12.6: Valuing an Index with High Growth

 

Dividends

Terminal value

Present Value

1

$40.00

 

$36.70

2

$44.00

 

$37.03

3

$48.40

 

$37.37

4

$53.24

 

$37.72

5

$58.56

$1,218.13

$829.76

Value of Index =

$978.59

Note that the dividends grow at 10% until year 5 and that the terminal value of the index is based upon a 4% growth rate forever.

Terminal value – 58.56 (1.04)/(.09-.04) = $1,218.13

            We noted one limitation of dividend discount models is that companies may not pay out what they can afford to in dividends or may choose alternative ways of returning cash to stockholders (stock buybacks, for instance). You can modify this model by replacing dividends with potential dividends (free cashflows to equity for the index) or by augmenting dividends with stock buybacks on the index.

Some Caveats

            While the building blocks for discounted cashflow valuation may remain the same for individual stocks and the markets, there are some cautionary notes that need to be added when valuing entire markets.

On the plus side, you should have less trouble forecasting earnings and dividends for an index than you should with individual stocks. After all, you have the luxury of diversification. In other words, you may over estimate earnings on some stocks and under estimate earnings on other stocks, but your overall measure of earnings can still be fairly precise.

Illustration 12.1: Valuing the S&P 500 using a dividend discount model: January 1, 2001

            On January 1, 2001, the S&P 500 index was trading at 1320. The dividend yield on the index based upon dividends paid in 2000 was only 1.43%, but including stock buybacks (from 2000) increases the composite dividend yield (dividends + stock buybacks) to 2.50%. Analysts were estimating that the earnings of the stocks in the index would grow 7.5% a year for the next 5 years. Beyond year 5, the expected growth rate is expected to be 5%, the nominal growth rate in the economy. The treasury bond rate was 5.1% and we will use a market risk premium of 4%, leading to a cost of equity of 9.1%:

Cost of equity = 5.1% + 4% = 9.1%

The expected dividends (and stock buybacks) on the index for the next 5 years can be estimated from the current dividends and expected growth of 7.50%.

Current dividends = 2.50% of 1320 = 33.00

 

1

2

3

4

5

Expected Dividends =

$35.48

$38.14

$41.00

$44.07

$47.38

Present Value =

$32.52

$32.04

$31.57

$31.11

$30.65

 

The present value is computed by discounting back the dividends at 9.1%. To estimate the terminal value, we estimate dividends in year 6 on the index:

Expected dividends in year 6 = $47.38 (1.05) = $49.74

Terminal value of the index =

Present value of Terminal value =

The value of the index can now be computed:

Value of index = Present value of dividends during high growth + Present value of terminal value = $32.52+32.04+31.57+$31.11+ $30.65+ $785 = 943

Based upon this, we would have concluded that the index was over valued at 1320. 

How well do intrinsic valuation models work?

            How well would a strategy of buying the index when it is intrinsically undervalued and selling when it is intrinsically overvalued do? It is difficult to answer this question because it depends upon the inputs you estimate for the intrinsic valuation model and your time horizon. Generally speaking, the odds of succeeding increase as the quality of your inputs improves and your time horizon lengthens. Eventually, markets seem to revert back to intrinsic value but eventually can be a long time coming.

            There is, however, a significant cost associated with using intrinsic valuation models when they find equity markets to be overvalued. If you take the logical next step of not investing in stocks when they are overvalued, you will have to invest your funds in either other securities that you believe are fairly valued (such as short term government securities) or in other asset classes. In the process, you may end up out of the stock market for extended periods while the market is, in fact, going up. For instance, most intrinsic value models would have suggested that the equity market in the United States was overvalued starting in 1994. If you had followed through and not invested in equities until 2002 (when the models suggested that valuations were fair again), you would have lost far more (by not investing in the bull market between 1994 and 2000) than you would have gained (by not investing in the down markets of 2001 and 2002).

            The problem with intrinsic value models is their failure to capture permanent shifts in attitudes towards risk or investor characteristics. This is because so many of the inputs for these models comes from looking at the past. Thus, the risk premium used to come up with the cost of equity may have been estimated looking at historical data on stock and bond returns and dividends may reflect what companies did last year. If one or both have changed as a consequence of shifts in the market, you will get a misleading signal from intrinsic valuation models. In fact, many investors who used intrinsic value models bought stocks during the early 1970s as stock prices dropped and failed to take into account the seismic shifts created by the high inflation of that period.

Relative Value Models

            In relative value models, you examine how markets are priced relative to other markets and to fundamentals. How is this different from intrinsic value models? While the two approaches shares some characteristics, it is less rigid, insofar as it does not require that you work within the structure of a discounted cashflow model.  Instead, you either make comparisons of markets over time (the S&P in 2002 versus the S&P in 1990) or different markets at the same point in time (U.S. stocks in 2002 versus European stocks in 2002).

Comparisons Across Time

In its simplest form, you can compare the way stocks are priced today to the way they used to be priced in the past and draw conclusions on that basis. Thus, as we noted in the section on historic norms, many analysts argue that stocks today, priced at 25 times earnings, are too expensive because stocks historically have been priced at 15-16 times earnings.

While reversion to historic norms remains a very strong force in financial markets, we should be cautious about drawing too strong a conclusion from such comparisons. As the fundamentals (interest rates, risk premiums, expected growth and payout) change over time, the PE ratio will also change. Other things remaining equal, for instance, we would expect the following.

In other words, it is difficult to draw conclusions about PE ratios without looking at these fundamentals. A more appropriate comparison is therefore not between PE ratios across time, but between the actual PE ratio and the predicted PE ratio based upon fundamentals existing at that time.

Illustration 12.2: PE Ratios across time for the S&P 500

            Figure 12.5 summarizes the Earnings/Price ratios for S&P 500, treasury bond rates and the difference between bond and bill rates at the end of each year from 1960 to 2000.

You do not need to be a statistician to note that earnings to price ratios are high (and PE ratios are low) when the treasury bond rates are high, and the earnings to price ratios decline when treasury bond rates drop.  This strong positive relationship between E/P ratios and T.Bond rates is evidenced by the correlation of 0.6854 between the two variables. In addition, there is evidence that the term structure also affects the E/P ratio. In the following regression, we regress E/P ratios against the level of T.Bond rates and the yield spread (T.Bond - T.Bill rate), using data from 1960 to 2000.

E/P = 0.0188 + 0.7762 T.Bond Rate - 0.4066 (T.Bond Rate-T.Bill Rate)      R2 = 0.495

            (1.93)      (6.08)                          (-1.37)        

Other things remaining equal, this regression suggests that

Š      Every 1% increase in the T.Bond rate increases the E/P ratio by 0.7762%. This is not surprising but it quantifies the impact that higher interest rates have on the PE ratio.

Š      Every 1% increase in the difference between T.Bond and T.Bill rates reduces the E/P ratio by 0.4066%.  Flatter or negative sloping term yield curves seem to correspond to lower PE ratios and upwards sloping yield curves to higher PE ratios. While, at first sight, this may seem surprising, the slope of the yield curve, at least in the United States, has been a leading indicator of economic growth with more upward sloped curves going with higher growth.

Based upon this regression, we predict E/P ratio at the beginning of 2001, with the T.Bill rate at 4.9% and the T.Bond rate at 5.1%.

            E/P2000 = 0.0188  + 0.7762 (0.051) – 0.4066 (0.051-0.049) = 0.0599 or 5.99%

            PE2000

Since the S&P 500 was trading at a multiple of 25 times earnings in early 2001, this would have indicated an over valued market.  This regression can be enriched by adding other variables, which should be correlated to the price-earnings ratio, such as expected growth in GNP and payout ratios, as independent variables. In fact, a fairly strong argument can be made that the influx of technology stocks into the S&P 500 over the last decade, the increase in return on equity at U.S. companies over the same period and a decline in risk premiums could all explain the increase in PE ratios over the period.

 



[1] For those unfamiliar with the Super Bowl, it is played between the winner of the American Football Conference (AFC) and the winners of the National Football Conference (NFC). It is played on the last Sunday in January.

[2] See Krueger and Kennedy, who claim to have been first to spot the correlation.

[3] Note that there are narrower versions of the January indicator, using just the first 5 or 10 days of January.

[4] Daily price volatility is estimated over four week windows. If the volatility in any four week window exceeds the volatility in the previous four-week window (at a statistical significance level of 99%), it is categorized as an increase in volatility.

[5] Chowdhury, Howe and Lin (1993) find a positive correlation between aggregate insider buying and market returns but report that a strategy based upon the indicator would not earn enough to cover transactions costs.

[6] See “Investor sentiment and Stock Returns’ by Fisher and Statman, Financial Analysts Journal, March/april 2000. They

 examined three sentiment indicators – the views of Wall Street strategists, investment newsletters and individual investors - and concluded that there is indeed evidence supporting a contrarian investment strategy

[7] Some of this table is extracted from Wood (1984).

[8] You could do a similar study using the level of treasury bill rates, but treasury bill rates were much lower prior to the second world war.