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

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
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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
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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
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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!
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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%
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Determinants of MRP
 If we understand the drivers of MRP we
may be able to estimate MRP more
precisely
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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
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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%
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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?
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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


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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
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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
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Imperfections coming down?

McGrattan and Prescott, 2000
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Imperfections coming down? .

Several Vanguard index funds charge less than 20bp fees
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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?
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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%
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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 =
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D1
r−g
© 2011 Ravi Jagannathan
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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
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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
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T
© 2011 Ravi Jagannathan
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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!
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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
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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



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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
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Time Series Models for Dividend Growth
Red: 45 degree line,
Rsq=9.10%
Blue: Fitted line,
Rsq=35%
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Time Series Models for Dividend Growth .
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ICC: Based on TS Model for Dividends
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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
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MRP Estimates: ReCap
 Require a model for future dividends
 Estimated MRPs: Vary substantially over time
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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
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© 2011 Ravi Jagannathan
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MRP Variations over time .
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MRP Variations over time ..
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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
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MRP: ICC Vs Graham & Harvey Survey
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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
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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
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Selected References

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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
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