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Does the Market Risk Premium (MRP) Change Over Time? Ravi Jagannathan Northwestern University & NBER Based on Work with Zhi Da, Soohun Kim and Jianfeng Shen July 2011 © 2011 Ravi Jagannathan 1 Why Should We Care? MRP measures economy wide reward for risk bearing Individual/Institutional Investors How much to save and how to allocate the savings across asset classes Corporations Influences investment decisions Regulation Affects prices charged by natural monopolies that are regulated July 2011 © 2011 Ravi Jagannathan 2 Historical MRP Average Real Returns on Stocks and Bills 1871-2009 1871-1940 1941-2009 # Years 139 70 69 Stocks 8.0% 8.0% 8.0% 1 Year Bills 2.8% 4.6% 1.0% MRP(Bills) 5.2% 3.4% 7.0% Std(MRP) 18.3% 19.9% 16.5% MRP (Bonds) 5.3% 4.1% 6.5% Data Source: Shiller, Robert J., http://www.econ.yale.edu/~shiller/data.htm July 2011 © 2011 Ravi Jagannathan 3 Historical MRP . Average MRP (Bills) in the two sub-periods 3.4% vs. 7.0% Std Dev of realized MRP 19.9% vs. 16.5% Std Dev of Average 1871-1940: 19.9%/√70 = 2.4% 1941-2009: 16.5%/√69 = 2.0% Even 70 years not enough to measure MRP with reasonable precision! The historical average MRPs of 3.4% & 7.0% are not statistically significantly different! July 2011 © 2011 Ravi Jagannathan 4 Historical MRP .. However , the difference between 3.4% & 7.0% is economically significant Example: Savings for retirement Suppose the risk free rate is 2%. Work for 20 years, put savings in equities. Buy an annuity at the risk free rate, and retire. Require half as much during 20 year retired life MRP = 3.4% => save 24% of income MRP = 7.0% => save 16% of income If savings are planned assuming an MRP of 7.0%, and actual MRP is 3.4%, then the expected shortfall of 39% at the time of retirement Corporate Investments MRP 7% will turn down most projects relative to MRP 3.4% July 2011 © 2011 Ravi Jagannathan 5 Determinants of MRP If we understand the drivers of MRP we may be able to estimate MRP more precisely July 2011 © 2011 Ravi Jagannathan 6 Determinants of MRP . Risk Economy wide pervasive risk How that risk is perceived Risk Aversion Ability to bear that risk Wealth distribution in the economy Age distribution in the economy When these change over time MRP is likely to change over time as well July 2011 © 2011 Ravi Jagannathan 7 Determinants of MRP .. What is a reasonable value for MRP, and how much can it vary over time? Mehra and Prescott (1985) A “Standard” Equilibrium “Model” of the economy Technology Preferences Perfect and complete markets Calibrate to match the US economy along certain dimensions MRP in the model economy is less than 1% July 2011 © 2011 Ravi Jagannathan 8 Determinants of MRP … The large Historical MRP relative to the Standard Model suggests that something else besides economy wide pervasive risk may be important driver of MRP What could be that something else? July 2011 © 2011 Ravi Jagannathan 9 Determinants of MRP …. That something is thought to be “Market Imperfections” (MI) Inability of investors to fully insure against risks outside of stock markets, viz. labor income risk Significant transactions costs in enforcing contracts Incomplete knowledge of opportunities Differential taxation of various types of income Reduction in imperfections July 2011 Some will increase the value of equities due to net cash flows to investors being higher Some will increase the value of equities due to lower MRP © 2011 Ravi Jagannathan 10 Determinants of MRP ….. Market Imperfections have become less important over time Improvement in information technology Easier access to information Easier to transact with others Easier to enforce contractual obligations More transparency Effectively lower tax on dividends Easier to diversify risks =>Lower effective perceived and real transactions costs => High cash flows to investors One time effect on prices, no effect on returns going forward => Lower MRP , lower returns going forward July 2011 © 2011 Ravi Jagannathan 11 Imperfections coming down? McGrattan and Prescott, 2000 July 2011 © 2011 Ravi Jagannathan 12 Imperfections coming down? . Several Vanguard index funds charge less than 20bp fees July 2011 © 2011 Ravi Jagannathan 13 Has the MRP Come Down? Fama and French (2002) Historical Average MRP (over short term bills) 1872-1950: 4.40% 1951-2000: 7.43% MRP has increased during the latter half! How to reconcile this with the reduction in market frictions leading to a decrease in the MRP? July 2011 © 2011 Ravi Jagannathan 14 Historical Vs Expected Return Going Forward When expected returns change over time historical averages can be a poor measure of the expected return going forward Consider a Console paying $10 per year A year back interest rate was 10% Price = $10/0.10 = $100 Now interest rate is 5% (unexpected change) Price = $10/0.05 = $200 Historical return ($200 +$10 - $100)/$100 = 110% Future return = 5% July 2011 © 2011 Ravi Jagannathan 15 Measuring Expected Return Going Forward Notation P: Stock Price; D: Expected Dividend; r: Discount rate for stocks; rf: risk free rate; MRP = r-rf Present Value relation D1 D2 P0 = + + ... 2 1 + r (1 + r ) When dividends grow at constant rate g, we get the Gordon Formula: P0 = July 2011 D1 r−g © 2011 Ravi Jagannathan 16 Measuring Expected Return . We can rewrite the Gordon Formula to get D1 r= + g ≡ dp + g P0 When dividends growth is not a constant, define g as the weighted average growth in dividends. Then, r = dp + g July 2011 © 2011 Ravi Jagannathan 17 Measuring Expected Return .. Suppose dividend growth rate is unpredictable and the current dividend growth rate is the best (but a very noisy) estimate of the future dividend growth Then mrpt = dpt + g t − rft Is a (noisy) but consistent estimate of MRP When MRP is a constant over some sample period, t = 1,2…T, a better estimate is: mrp / T ∑ t 1 ( dpt + gt − rft ) / T = ∑ t 1= ( rt − rft )= = T July 2011 T © 2011 Ravi Jagannathan 18 Measuring Expected Return … Fama and French (2000) Historical Average MRP (over short term bills) 1872-1950: 4.40% 1951-2000: 7.43% Gordon Model based MRP: 1951-2000: 2.55% Payout form changed during 1951-2000 period Stock repurchases became more common Use earnings growth instead of dividend growth 1951-2000: 4.32% Lesser imperfections probably increased net cash flow to investors, raised equity values, but not had much of an effect on MRP! July 2011 © 2011 Ravi Jagannathan 19 Using Better Dividend Forecasts Present Value Relation D1 D2 P0 = + + ... 2 1 + r (1 + r ) If we can predict future dividend growths better (than assuming that the best predictor is the current dividend growth rate), we can use the present value relation to estimate the discount rate for equities and from that the MRP July 2011 © 2011 Ravi Jagannathan 20 Using Better Dividend Forecasts. Method 1 Make use of analysts’ forecasts for earnings for next 5 years Assume that growth rate will taper over time Based on productivity of capital. D/E, and the growth in earnings forecast the dividends payout Estimate the discount rate for stocks (Implied Cost of Capital, ICC) from the present value relation Method 2 July 2011 Build a time series model for forecasting dividends that uses historical information on past dividends, past dividend to price ratio, etc Use the forecasts of future dividends from the time series model to estimate the discount rate on stocks (ICC) Use a linear approximation of the present value relation for computational ease © 2011 Ravi Jagannathan 21 Time Series Models for Dividend Growth Red: 45 degree line, Rsq=9.10% Blue: Fitted line, Rsq=35% July 2011 © 2011 Ravi Jagannathan 22 Time Series Models for Dividend Growth . July 2011 © 2011 Ravi Jagannathan 23 ICC: Based on TS Model for Dividends July 2011 © 2011 Ravi Jagannathan 24 TS vs. ROE/Payout Ratio Models for Dividends Left panel: MRP = TS ICC- Rf. Assume a real risk free return of 3% prior to 1997; and TIPS rate for latter periods Right panel: From Campbell (2007). Solid line assumes ROE of 6% and D/E of 50%; Dotted line uses a 3 year MA of ROE and D/E July 2011 © 2011 Ravi Jagannathan 25 MRP Estimates: ReCap Require a model for future dividends Estimated MRPs: Vary substantially over time July 2011 © 2011 Ravi Jagannathan 26 MRP Estimates: Variations over time Relation to Stock market volatility? Expect a positive relation Investor sentiment? Expect a negative relation If prices are bid up due to “irrational exuberance” MRP estimates based on time series models will be downward biased estimates of what investors expect to get July 2011 © 2011 Ravi Jagannathan 27 MRP Variations over time . July 2011 © 2011 Ravi Jagannathan 28 MRP Variations over time .. July 2011 © 2011 Ravi Jagannathan 29 MRP from Surveys MRP = (ICC-LT Bond Yield) is low in 1999 but MRP from Survey high suggests irrational exuberance or structural shift not captured by time series model for dividends Year 1997 Welch Survey MRP 6.5% MRP 2.5% 1998 1999 2000 2001 2.2% 2.9% 6.9% 2.4% 2.2% S&P500 Return 31.0% 26.7% 19.5% -10.1% -13.0% Nasdaq Return 22.0% 29.3% 83.6% -39.4% -20.8% Realized SD 15.8% 18.6% 15.5% 18.1% 17.7% *Welch survey MRP is relative to Bills – so we subtract 0.70% in 1997 and 0.60% in 1999 July 2011 © 2011 Ravi Jagannathan 30 MRP: ICC Vs Graham & Harvey Survey July 2011 © 2011 Ravi Jagannathan 31 Summary/Implications MRP varies over time Estimates of MRP not very reliable During the stock market bubble period of the Nineties, MRP based on time series models of dividends provide much lower estimates than surveys During bubble periods: Investors with expectations similar to Surveys will be disappointed Regulators who make decisions based on rational models of MRP may not be able to attract sufficient capital Firms making rational investment decisions will not be able to meet market expectations July 2011 © 2011 Ravi Jagannathan 32 Summary/Implications . MRP varies over time MRP estimates are imprecise => Need for taking the imprecise nature of MRP estimates into account when making decisions Rule of thumb: MRP = 4.5% Based on Fama and French, 2000 1872-1950: 4.40% 1951-2000: 4.32% May be OK for long term investments When more precise estimate of MRP is needed Go to the market and raise the funds July 2011 See what MRP investors need! © 2011 Ravi Jagannathan 33 Selected References Campbell, John Y. and Robert Shiller, Review of Financial Studies, Fall 1988 Campbell, John Y., Estimating the equity premium, NBER Working Paper 13423 Graham, John R., and Campbell R. Harvey, The long-run equity risk premium, Finance Research Letters, 2, 2005 Fama, Eugene F. and Kenneth R. French, The equity premium, Journal of Finance, April 2002. Jagannathan, Ravi Ellen McGrattan and Anna Scherbina, Quarterly Review of the Federal Reserve Bank of Minneapolis, Fall 2000 Lee, Charles M.C., James Myers, and Bhaskaran Swaminathan, Journal of Finance, October 1999 Mehra, Rajnish and Edward C. Prescott, The equity premium: A puzzle, Journal of Monetary Economics, March 1985 Pastor, Lubos, Meenakshi Sinha, and Bhaskaran Swaminathan, Estimating the intertemporal risk-return tradeoff using the implied cost of capital, Journal of Finance, November 2008 July 2011 © 2011 Ravi Jagannathan 34