does the market risk premium (mrp) change over time? by professor ravi... · mrp varies over time...

July 2011 © 2011 Ravi Jagannathan 1

Does the Market Risk Premium (MRP) Change Over Time?

Ravi JagannathanNorthwestern University & NBER

Based on Work with Zhi Da, Soohun Kim and Jianfeng Shen


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


Historical MRP

Average Real Returns on Stocks and Bills1871-2009 1871-1940 1941-2009

# Years 139 70 69Stocks 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


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!


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%


Determinants of MRP

If we understand the drivers of MRP we may be able to estimate MRP more precisely


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


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%


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?


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 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


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


Imperfections coming down? McGrattan and Prescott, 2000


Imperfections coming down? . Several Vanguard index funds charge less than 20bp fees


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?


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%


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

When dividends grow at constant rate g, we get the Gordon Formula:

( )...

11 221

0 ++

++

=r

Dr

DP

grDP−

= 10


Measuring Expected Return .

We can rewrite the Gordon Formula to get

When dividends growth is not a constant, define as the weighted average growth in dividends.

Then,

gdpgPDr +≡+=

0

1

gdpr +=

g


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

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:

ftttt rgdpmrp −+=

( ) ( )1 1/ /T T

t ft t t ftt tmrp r r T dp g r T

= == − = + −∑ ∑


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!


Using Better Dividend Forecasts

Present Value Relation

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

( )...

11 221

0 ++

++

=r

Dr

DP


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

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


Time Series Models for Dividend Growth

Red: 45 degree line, Rsq=9.10%

Blue: Fitted line, Rsq=35%


Time Series Models for Dividend Growth .


ICC: Based on TS Model 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

TS vs. ROE/Payout Ratio Models for Dividends


MRP Estimates: ReCap

Require a model for future dividends Estimated MRPs: Vary substantially over time


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


MRP Variations over time .


MRP Variations over time ..

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

*Welch survey MRP is relative to Bills – so we subtract 0.70% in 1997 and 0.60% in 1999

© 2011 Ravi Jagannathan 30July 2011 30

Year 1997 1998 1999 2000 2001

Welch Survey MRP 6.5% 6.9%

MRP 2.5% 2.4% 2.2% 2.2% 2.9%

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%

MRP from Surveys

July 2011


MRP: ICC Vs Graham & Harvey Survey


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


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

See what MRP investors need!


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

does the market risk premium (mrp) change over time? by professor ravi... · mrp varies over time...

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