SORTING THE PIECES TO THE EQUITY RISK PREMIUM PUZZLE

Transcription

1 Market Eiciency Eicient markets Can t use ast rices to redict uture rices excet through ricing models like CAPM. No systematic abnormal returns. Strong orm: All ublic and rivate inormation is ully embedded in stock rices. Verges on tautology in deinition o abnormal erormance: What are abnormal returns to inormation collection? Firm s return should be redicted by β In an u-year, highest β irms should have highest returns In a down-year, highest β irms should have lowest returns Regress monthly returns or ten irms or 5 years on the market. Sort by estimated βs. Comare to actual returns. Other actors such as book-to-market and size may consistently orecast returns, but these can be included in a ricing model so should not be called anomalies. Anamolies January eect: January returns, es. or small stocks, are too high. => Buy in December and sell in January. Weekend eect: Monday returns are too low. => Sell on Friday and buy on Monday. S&P eect: Sell short and hold on??? Wednesday eect: Volatility over Wednesday when market is closed on Wednesday lower than volatility when market is oen. Etc. Noise traders v. Smart money 1 Arbitrage(u)rs ush rice to equilibrium. Buy when rices too low and sell short when rices are too high. Risk: (a) undamental; (b) misricing duration. Liquidity requirements or correcting tye (b). May be able to set relative rices but hard to set overall level o rices no arbitrage object. Investor Sentiment: Trend chasing / ads / guru analysis / technical analysis (hd & shoulders) / stock broker advertisements / How do noise traders survive? Carry too much risk and are comensated or it. (Sel ulilling rohesy.) Emirical evidence: Mean reversion. Stock returns are more volatile than cash lows. However, volatility is redictable. 2 Some reerences: Black, "Noise," Journal o Finance 41 (1986) Harris & Gurel, "Price and Volume Eects Associated with Changes in the S&P 500 List: New Evidence or the Existence o Price Pressures," Journal o Finance 41 (1986) Kleidon, Anomolies in Financial Markets, Journal o Business, 1986, 59, Sul Mitchell & Mulherin, "The Imact o Public Inormation on the Stock Market," Journal o Finance 49 (1994) Shleier & Summers, "The Noise Trader Aroach to Finance," Journal o Economic Persectives 4 (1990) Bertonazzi & Maloney, Does Imlied Volatility Imly Volatility -- In Bonds?, Journal o Fixed Income, December 2001.

2 SORTING THE PIECES TO THE EQUITY RISK PREMIUM PUZZLE I. Introduction BY ERIC BERTONAZZI & M.T. MALONEY The equity risk remium, that is, the amount by which equities outerorm ixed income securities, continues to uzzle inancial analysts. The drama has heightened in the 1990s and esecially in the last ew years as the equity market has recorded record returns. Price to earnings ratios are at an all time high. It is not out o academic curiosity that analysts try to understand this conundrum. I the increase in stock rices relects a higher return that is due to equities because o higher risk, then a dooms-day reckoning lurks somewhere on the horizon. That is, i the enormous returns to equities in the 1990s are the just reward to holding these risky assets, then a downturn o some vaguely similar roortion has to be recognized as a realistic ossibility. On the other hand, the stock rice run-u that we have seen in the last several years may simly relect a re-ricing o assets in light o changing conditions. As such, it is an unexected change the rice level not the exected return to holding these assets. In articular, i the true underlying risk o equity has actually allen or i the exected growth rate o earnings has dramatically increased, then the stock rice run-u o the 1990s is a once-and-or-all adjustment in the rice level, a ortuitous coincidence or those holding equities during this eriod, but one not likely to be reeated. From the ersective o ortolio decision-making, neither ossibility is articularly glamorous. On the one hand, a stock market crash may loom over equity dominated ortolios. On the other, the return to equity relative to ixed income assets will not be as large in the uture as it has been in the ast. Nonetheless, an answer to the question is imortant. I the undamental risk o equities is truly relected in the large ositive returns enjoyed over the last several years, then rudent investors should seriously consider shiting a substantial ortion o their assets to ixed income securities. On the other hand, i these large ositive returns have been the result o rice level adjustment, then there is every reason to leave assets in equities even though they will not continue to enjoy the magnitude o returns exerienced in the ast. The urose o this work is to resent some emirical evidence that weighs in on this question. Something has changed. We attemt to determine the most likely ossibility. II. Setting the stage The equity risk remium is the amount by which equities outerorm ixed income securities. It comes rom the Caital Asset Pricing Model (CAPM). CAPM says that investors choose between the risk ree security and a market ortolio o all risky assets. The exected return on any one risky asset minus the risk ree yield is equal to the covariance o that risky asset with the market divided by the variance o the market times the dierence between the exected return or the market minus the risk ree return. That is, [ E( r ) r ] = β [ E( r ) r ] i i m 2

3 where beta is the covariance o asset i with the market divided by the variance o the market. [ E( r ) r ] is the equity risk remium (ERP). Oerationally, CAPM identiies the exected m return on a security as: E( r ) = β ERP + r. i i This exected return is the value by which the exected uture cash lows accruing to the security holders are roerly discounted. The ieces o the equity risk remium uzzle can be laid out in an orderly ashion by considering the constant growth model o stock rices. Assets with an indeinite lie and an initial cash low that grows at a constant rate over time can be riced by discounting this uture cash lows. When we consider the market ortolio o all risky assets or which beta is 1, the ormula is: P = E ERP + r g where P is the asset rice, E is the current level earnings, ERP is the equity risk remium, r is the risk ree return, and g is the growth rate o earnings. For ractical uroses we can think o P as the index value o the S&P 500 and E is the sum o the earnings or all o these securities. They are exected to grow at a constant rate, g, starting rom the current value. The discount rate alied to these earnings is ERP + r. The discount and growth rates in the denominator are in real terms. The exected rate o inlation can be added to the discount rate to make it nominal, but then it must also be added to the growth rate. Hence, exected inlation cancels out o the equation. We will reintroduce exected inlation into the discussion at a later oint, but recognize here that its direct eect is a wash. For the urose o setting the stage or our discussion, it is useul to rewrite the constant growth model in terms o the inverse rice to earnings ratio. That is, 1 P / E = ERP + r g The inverse o the rice to earnings ratio, or earnings to rice (E/P), is a ercent. In this ormulation we can comare the market valuation o rice relative to earnings with the comonent ieces, real growth, the real risk ree rate, and the equity risk remium. The measurement o the ERP is o some interest. Historical data are commonly used. The average annual return on caitalized value o widely traded securities rom 1926 through 1998 is 10.8 ercent. This is shown in Table 1. Also shown there is the average annual return on 20 year U.S. Government Treasury bonds. Their average annual return is 2.5 ercent. One estimate o the ERP is the simle dierence between these. Another is the average o annual dierence between these. The two are nearly the same. This value is slightly higher than 8 ercent. The variance o the government long bond return is itsel interesting. The standard deviation o this return is over 10 ercent. This seems hardly a reasonable roxy or a risk ree return. While government bonds are virtually deault risk ree (at least in the U.S.), they are not 3

4 risk ree in other dimensions. Notably, inlation signiicantly reduces the return on ixed income securities. Fixed income securities, because they ay a nominally denominated couon and redemtion, are articularly sensitive to inlation. One way to assess the inlation comonent o government bond yields is to look at the return on the recently issues inlation rotected bonds called TIPS (treasury inlation rotected securities). Yields on these 10 year notes are shown in Figure 1. Also shown there are similar term regular bonds and the dierence. Notice that the bounce in the yields on TIPS is much more damed than on regular bonds. Moreover, the variance o the yield on the dierence between regular yields and TIPS yields is the largest. This imlication is that inlation is the biggest comonent o variance in the yield on government bonds. The yield on TIPS has moved some. Over the eriod o mid 1997 through mid 1999 it moved rom 3.3% to around 4 ercent. There is some risk even in inlation rotected U.S. government bonds. The deault risk is de minimus. However, there is variance due to changes in the real discount rate and in suly and demand o this security as the deault security or light away rom risk as was exerienced during the eriod o the Russian bond crisis. Figure 1 Treasury Inlation Protected Security 8.0% 7.0% 6.0% 5.0% Yield 4.0% 3.0% 2.0% 1.0% 0.0% Mar-97 Jan-97 May-97 Jul-97 Se-97 Nov-97 Jan-98 Mar-98 Date May-98 Jul-98 Se-98 Nov-98 Jan-99 Mar-99 May-99 TIPS Govt Note (2/15/07) TIPS minus Notes The imortant oint is that the real risk ree rate is embedded in the yield on TIPS. That yield is currently around 4 ercent, and it has not varied largely over the last two years. A reasonable imlication is that the real risk ree rate both historically and looking orward is somewhere around 4 ercent. This conclusion is seculative but not wild-eyed. Looking back at the historical return on government bonds, it hard to exlain negative returns excet on the basis o inlation that was unexected or, worse, unrotectable. I it was just unexected, then ossibly the 2.5 ercent realized return over the last 75 years was the exected return and the current 4 ercent is unusually high. However, an alternative exlanation is that inlation is a cancer against which there is not erect rotection. By this line o logic, the 4 ercent we see now is the real 4

5 return that was always exected rom government bonds and the dierence between the exerience 2.5 ercent and the 4 ercent that is now enjoyed is thet o the most dreadul sort. III. Examining the Comonents I the market ortolio is rationally riced, then the comonents o the constant growth model have to add u. 3 Some ossibilities are outlined in the ollowing table: Table 2: Possible Combinations o Equity Risk Premium and Real Growth that Satisy the Constant Growth Formula Today s P/E = 33 Inverse P/E = Equity Risk Premium + Real Risk-Free Rate - Real Growth Rate 3% = 1% + 4% - 2% 3% = 3% + 4% - 4% 3% = 6% + 4% - 7% 3% = 8% + 4% - 9% Other values outside these limits are ossible, but the oint is that the equation has to hold. Unless the market ricing o equities is irrational, there must be a balance between the equity risk remium and the exected real growth o earnings given the current real risk-ree rate. On one hand it may be the case that the exected rate o real growth in the economy is unchanged since The real growth rate that we were exeriencing in 1994 o around 2 ercent was a value that had maintained or most o the ost WWII eriod. Arguably, this is a long-run constant. I the exected real growth in the economy today is 2 ercent, it imlies that the equity risk remium has allen rom the historical average since 1926 o around 8 ercent to 1 ercent today. On the other hand, i the equity risk remium is unchanged rom its historical level, then it would take a real growth rate o 9 ercent to validate the current rice-earnings ratio. Possibly the historical equity risk remium is overstated because the real discount rate has been undervalued due to inlation. One way to calculate the equity risk remium is to take the historical market return and subtract the current real government bond rate. This gives an equity risk remium o around 6 ercent. Still, a 6 ercent equity risk remium requires a real growth rate o 7 ercent to justiy the current value o the market relative to orecast earnings. Real growth rates o 9 ercent or even 7 ercent are almost out o the question, 4 but it is ossible that real growth has increased. Say that it is now 4 ercent. FED Chairman Greensan suggested that it might be this high in a recent seech. This would mean that the equity risk remium has allen to 3 ercent. 3 At least on average. The rice earnings ratio can vary over time due to stochastic variation in the timing o cash lows. P/E is simly a snashot that catures the current rice o assets and the near-term level o earnings. 4 To ut 9 ercent growth in ersective, a middle-class amily earning $50,000 today would be making more than $600,000 in real terms in a generation. 5

6 III. What does it mean? Does it make sense that the equity risk remium may have allen to 1 or 2 ercent? Possibly. [Give some rationalizations here.] Does it make sense that the real growth rate in the economy has increased to 7 ercent? This is very unlikely. Real growth o this magnitude has only been exerienced a ew times in the history o mankind. [ MORE Here] However, it is somewhat more likely that the real rate o growth can be exected to be 4 or 5 ercent in the uture. I this is true it is a dramatic event. It means that real incomes will double every??? years. It imlies national wealth and welare that were the dream o the 1960s but desaired o since. To believe this scenario, we have to ask ourselves how the real growth rate o the economy could have essentially doubled in the last ive years. One ossible answer links real growth to government olicy esecially in the arena o monetary olicy. [Lower inlation and ermanent inlation rotection => real growth.] [Technological rogress through comuters.] [Realization o these ossibilities, i.e., resolution o uncertainty.] I the real growth rate has increased some, it still means that the equity risk remium has allen. What might account or this? (a) Reduction in inlation risk. (b) Better monitoring. (c) More secure roerty rights system. The imlications o any o the various scenarios are roound or society and or individual investors. For instance, i the equity risk remium has truly allen to 1 ercent, the otimal ortolio strategy has changed dramatically or retired eole and eole close to retirement. [MORE ] IV. Sorting Through the Evidence What we want to do is use the available evidence to give us a clue as to which o the ossible scenarios is most likely. To this end, we hyothesize that the equity risk remium is a unction o several variables. What we then do is obtain statistical estimates o the arameters describing the relation between the equity risk remium and observable actors. This gives us a orecast o the equity risk remium and then, by inerence, the exected real growth rate o earnings. Arguably, the equity risk remium is a unction o many things. We suggest that it may be determined by demograhics and technology; it may be a unction o the real risk-ree rate o interest; it is likely a unction o inlation exectations; and inally, it may be a unction o the undamental level o risk in the market. We are able to obtain emirically observable roxies or many o these actors. First, let s discuss the nature o the relations. Demograhics and Technology [PUT IN A DISCUSSION OF DEMOGRAPHICS AND TECHNOLOGY] The Real Risk-Free Rate 6

7 In order to describe the relation between the equity risk remium and the risk ree return, it is useul to visualize this using the simle Caital Asset Pricing Model. Figure 2 shows the standard CAPM equilibrium. The bullet-shaed curve is made u o all ossible combinations o all risky assets. That is, assume that an investor holds some o each risky asset but holds them in dierent roortions. As the relative roortions change, the exected return and risk or the ortolio changes. The bullet is the ma o all o those ossible combinations. The straight line (called caital market line ) connects the bullet at its highest oint with the risk-ree asset. The ortolio o any articular investor is balanced by holding more or less o the risk-ree asset and the ortolio o risky assets associated with the tangency o the bullet and the caital market line. There is one otimal ortolio o risky assets; it is the one that yields the highest return relative to the risk reduction oortunity aorded by the risk-ree asset. Thus, all assets are riced so that they it into this otimal ortolio. The vertical height o this oint on the bullet is the market rate o return earned by holding this ortolio o equities. The dierence between this market return and the risk-ree return is the equity risk remium. Figure Risk-Return Frontier The Bullet: Variation in Risk and Return with resect to ortolio weights Exected Return Risk (standard deviation) The Bullet Caital Market Line Notice what haens as the risk-ree return changes. Assume that the risk-ree return alls to zero. The otimal ortolio changes as the tangency o the caital market line slides down and to the let along the bullet. The market return on the otimal ortolio alls, but not as much as the decline in the risk-ree asset. This causes the ga between the market return and the risk-ree return to increase. This means that the ortolio re-balancing behavior o investors described by the CAPM in a direct sense negatively relates the equity risk remium to the risk-ree return. Also, the equity risk remium may ossibly be related to the risk-ree return through eedback eects. That is, changes in the risk-ree return may change the shae o the bullet itsel. The roblem is, we do not have a clear theory about how such eects might occur and what direction their imact might be. One roblem with the CAPM, as well as other asset ricing models, is that we do not have erect measures o the variables described in the model. For instance, there is not such thing as a ortolio o all risky assets. As a roxy, we use broad-based ortolios o large comanies, such as the S&P 500. Similarly, there is no truly risk-ree asset. Long term government bonds are close, but they do have some risk. Most imortantly, government bonds are at risk to inlation. Emirically, this may be imortant because it means that changes in exectations about inlation 7

8 can change the risk-ree return and they are also likely to change the shae o the bullet. Hence, emirically we exect there to be a relation between the equity risk remium and the risk-ree return over and above that described by the CAPM. Fundamental Risk [Discuss the VIX] Inlation V. Statistical Analysis The emirical estimates are obtained in the ollowing way. Daily values o the ercentage change in the S&P 500 index otion rice are regressed on the ercentage change in earnings, the change in the VIX, change in an inlation rotected government bond yield, and the change in exected inlation. The ercentage change in the S&P 500 index otion rice is a measure o the rate o return enjoyed by holding a value-weighted ortolio o equities. The VIX is the imlied variance o the S&P 100 Index Otion derived using the Black-Scholes ormula. 5 We use the twelve month trailing earnings or the S&P 500 irms. The new U.S. Treasury inlation rotected securities (TIPS) oer a unique estimate o the real risk-ree rate. There is virtually no deault risk on U.S. government bonds. However, the risk o inlation does aect the value o the securities. TIPS with 10 year maturities have been issued since We ollow the yield on the January 15, 2007 maturity bond. At the same time, we measure inlation exectations by taking the dierence between this TIPS yield and the yield on an unrotected bond issued at around the same time. 6 The TIPS data limit the samle used in the estimate to the eriod February 1997 through June However, we use longer time series on other variables or illustration and tests o robustness. Figure 3 lots the value o the S&P 500 Index Otion rom 1989 through 1999 along with the trailing 12 month earnings or the S&P 500 irms. As can be seen in the grah, both the value o the index and earnings have risen over the eriod, though their movements are not in locked ste. 5 The imlied variances on the nearest to the money two month and our month S&P 100 index ut and call are calculated. There is a high degree o correlation between the S&P 500 and 100 otions. 6 The inlation unrotected security is a standard treasury 10 year bond with a February 15, 2007 maturity. The inlation rotected bonds have not been on the market long enough or a constant maturity yield series to be ublished. 8

9 Figure 3 Index Otion Value and Earnings or the S&P Index Otion Earnings Jan-89 Ar-89 Aug-89 Nov-89 Mar-90 Jun-90 Oct-90 Jan-91 May- Se-91 Dec-91 Ar-92 Jul-92 Nov-92 Feb-93 Jun-93 Se-93 Jan-94 May- Aug-94 Dec-94 Mar-95 Jul-95 Oct-95 Feb-96 Jun-96 Se-96 Jan-97 Ar-97 Aug-97 Nov-97 Mar-98 Jul-98 Oct-98 Feb-99 May S&P 500 Earnings Similarly, Figure 4 shows the VIX and the yield on 30 year treasury bonds. The long-term government bond rate has exhibited a declining ath over the samle eriod. On the other hand, the VIX has bounced around a good bit, but there is no obvious trend. Figure 4 9

10 The regression results are resented in Table 3. All the right-hand side variables have the exected signs and each is highly signiicant. The regression was analyzed or lagging and leading eects but virtually nothing was ound. 7 Table 3: Regression Results Deendent Variable: % Change in S&P 500 Otions Index Indeendent Variable Parameter t-stat Intercet % Change in Earnings Change in VIX Change in LT Govt Bond Yield R 2 :.597; Obs: 2561; Mean deendent var.0006 The magnitude o the coeicient on the ercentage change in earnings is too small. The value is.077; this means that i earnings double, the value o the S&P increases by 7 ercent. As we discussed above, the coeicient value should theoretically be somewhat larger than one. However, the measurement o earnings in our data is only weakly linked to the theory. Theoretically, stock rices relect exected uture earnings. The earnings measure that we use is the announced levels o ast earnings. So it is reasonable that the it is less than erect. Because the variable has the correct sign and is statistically signiicant in exlaining variation in the equity rate o return, we leave it in the regression. The major contributor to the it o the regression is the VIX. As the VIX increases, stock rices decline. The coeicient value says that i the VIX changes by 10 oints, which is slightly less than two standard deviations, stock rices all by around 5 ercent. The VIX has varied between 9 and 48 over the last decade. It current stands at 25. Adding the T-bond yield to the regression boost the R 2. A change in the yield on long-term government bonds by one ercentage oint (aroximately one standard deviation) causes a 3 ercent change in the S&P index. Long term yields are currently around 6 ercent. They have been as low as 4.7 and as high as 9.3 during the last decade. VI. Inerring the Equity Risk Premium and the Real Growth Rate We now have enough inormation to calculate the equity risk remium as it described by equation (4). The values o the linear coeicients in equation (4) can be taken rom the estimated regression. They are: = V P / E 7 It is a bit surrising that there were none on the earnings variable. We might exect some re-announcement leaks. Just looking at the data, there seem to be some, but nothing turns out to be there statistically. 10

11 32. r = 1 P / E Thus, the equity risk remium can be exressed in terms o an initial value and the current values o the rice/earnings ratio, the VIX, and the long-term government bond rate: r F HG = r + P E V r / P / E Let s assume that the initial value o the equity risk remium is 7.5 ercent. This was the value reorted by Ibbotson in In this sense, we can think o equation (5) as describing the evolution o the equity risk remium since that time based on changes in the VIX and the government bond rate. From where we stand now, the P/E is around 33, the VIX is around 25, and the long-term government bond rate is around 6 ercent. Based on these numbers, the current value o the equity risk remium is 2.4 ercent. Similarly, we can solve or the growth rate o earnings that is imlied by the rice/earnings ratio that we observe today. Substituting equation (5) into the constant growth model gives: Rewriting, we solve or g: P E 1 = r P E V 32. P E r g + + / / I K J g = r + ( V r 1) 2 P / E 0 1 Again using 7.5 or the initial value o the equity risk remium, and given the current P/E o 33, the VIX o 25, and the long-term government bond rate o 6 ercent, the imlied growth rate in uture earnings is 5.4 ercent. V. Conclusions Our conclusion is that the equity risk remium has declined rather dramatically over the last decade. This is not a new idea; other researchers have said much the same. However, we add some new insight by linking changes in the equity risk remium to changes in the risk ree return and a measure o the undamental risk o equities. Based on these relations and on the levels o the risk ree return and the undamental risk, we eg the equity risk remium at 2.5 ercent. We also calculate the exected growth in earnings. We ind that this value is 5.4 ercent. These imlied value o the equity risk remium is substantially dierent rom its long-term estimated value. However, this is the value necessary to rationalize the current state o the economy. The emirical estimates account or the market s estimate o the underlying riskiness o 1 11

12 equity returns and the relationshi between this equity risk-return tradeo and the risk-ree return. Assuming that the market is rationally ricing assets as measured in the observed rice/earnings ratio, the run-u in value during the 1990s imlies that the return to equity over government bonds will be markedly lower in the uture. 12

13 APPENDIX A: The Emirical Dimensions o the Constant Growth Formula In order to make the constant growth model emirically useul, we take the natural logs o ormula. The change in a natural log is the ercentage change in the level o the variable. In logs, the constant growth ormula is: ln P = ln E ln( r + r g) which says that the market rate o return is a unction o these various actors. Embodied in this are the relations between the equity risk remium and its determinants. This can summarized in the ollowing ormula: r = ( V, r, I, D) where V is level o undamental risk in the market as measured by the VIX, r is the real risk-ree rate, I stands or inlation exectations, and D is the dividend ayout (?) rate, which catures the level o technological rogress. Taking derivatives with resect to the variables o interest gives: ln P ln E g ( E) E = 1+ 3 r + r g ln P 1+ r = r r + r g ln P V = V r + r g ln P I = I r + r g ln P D = D r + r g Equations (1)-(3) are imortant because they can be estimated statistically. The let-hand side terms are ound by regressing the ercentage change in the S&P 500 index on the ercentage change in earnings, the change in the inlation-rotected, long-term government bond rate, exected inlation, the change in the VIX, and the change in the dividend ayout rate. 13

14 Date Market Caitalization Table 1: Returns on the Market and on Bonds Market Dierence Return 20 yr. U.S. Treasury Bond Yield Bond Value ,890, % 30,890, ,438, % 11.0% 26.4% 34,297, ,242, % 1.0% 36.2% 34,654, ,734, % 3.2% -9.2% 35,766, ,937, % 10.7% -35.9% 39,586, ,402, % 4.2% -51.9% 41,249, ,319, % 27.1% -41.5% 52,444, ,951, % -0.6% 53.2% 52,140, ,543, % 8.0% -5.9% 56,306, ,068, % 2.0% 38.4% 57,432, ,821, % 6.3% 23.0% 61,044, ,521, % -2.9% -34.4% 59,286, ,459, % 8.3% 16.1% 64,201, ,575, % 6.4% -8.6% 68,329, ,892, % 5.3% -17.1% 71,957, ,786, % -8.8% -5.8% 65,632, ,382, % -6.1% 14.8% 61,642, ,175, % -1.1% 25.2% 60,958, ,765, % 0.7% 15.7% 61,384, ,932, % 8.5% 26.1% 66,590, ,038, % -1.8% -2.8% 65,375, ,541, % -11.6% 12.5% 57,765, ,042, % 0.7% -3.1% 58,152, ,229, % 8.3% 7.3% 62,949, ,545, % -5.7% 31.1% 59,336, ,484, % -9.8% 28.4% 53,515, ,983, % 0.3% 10.1% 53,660, ,982, % 3.0% -5.7% 55,264, ,308, % 7.7% 39.4% 59,509, ,019, % -1.6% 25.2% 58,533, ,994, % -8.4% 16.5% 53,592, ,606, % 4.5% -15.8% 55,977, ,449, % -7.9% 50.5% 51,566, ,952, % -3.8% 15.8% 49,612, ,275, % 12.3% -12.5% 55,719, ,066, % 0.3% 26.1% 55,881, ,100, % 5.7% -11.4% 59,049, ,542, % -0.5% 18.3% 58,783, ,073, % 2.3% 13.1% 60,135, ,584, % -1.2% 14.0% 59,396, ,534, % 0.3% -10.6% 59,568, ,543, % -12.2% 39.1% 52,283, ,348, % -5.0% 19.3% 49,679, ,083, % -11.2% 0.4% 44,130, ,893, % 6.6% -6.8% 47,051, ,511, % 9.9% 6.9% 51,700,533 14

15 1972 1,006,944, % 2.3% 32.5% 52,863, ,132, % -9.9% -10.1% 47,640, ,804, % -7.9% -23.7% 43,901, ,743, % 2.2% 32.4% 44,858, ,712, % 11.9% 12.2% 50,214, ,930, % -7.4% 1.4% 46,488, ,698, % -10.2% 14.0% 41,741, ,068,109, % -14.5% 33.4% 35,676, ,384,989, % -16.4% 46.0% 29,836, ,288,033, % -7.1% 0.1% 27,724, ,470,731, % 36.5% -22.3% 37,843, ,821,720, % -3.1% 27.0% 36,666, ,757,939, % 11.5% -15.0% 40,890, ,195,913, % 27.2% -2.3% 52,008, ,467,298, % 23.3% -11.0% 64,131, ,467,791, % -7.1% 7.1% 59,571, ,702,044, % 5.3% 4.2% 62,705, ,290,804, % 13.5% 8.3% 71,145, ,970,824, % 0.1% -9.8% 71,216, ,982,063, % 16.2% 17.8% 82,746, ,375,078, % 6.4% 3.5% 88,025, ,020,231, % 15.5% -0.7% 101,660, ,964,997, % -10.5% 9.3% 91,037, ,732,165, % 29.0% 6.6% 117,438, ,237,516, % -4.3% 26.6% 112,447, ,699,532, % 14.2% 15.7% 128,380, ,175,870, % Average 10.8% 2.5% 8.1% Std Dev 20% 11% 22% Equity Risk Premium Average Market Return minus Average Bond Yield 8.3% Average o Dierence 8.1% 15