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An Updated Equity Risk Premium: January 2015
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Base year cash flow (last 12 mths)Dividends (TTM): 38.57+ Buybacks (TTM): 61.92
= Cash to investors (TTM): 100.50Earnings in TTM: 114.74
Expected growth in next 5 yearsTop down analyst estimate of earnings
growth for S&P 500 with stable payout: 5.58%
106.10 112.01 118.26 124.85 131.81 Beyond year 5Expected growth rate = Riskfree rate = 2.17%
Expected CF in year 6 = 131.81(1.0217)
Risk free rate = T.Bond rate on 1/1/15= 2.17%
r = Implied Expected Return on Stocks = 7.95%
S&P 500 on 1/1/15= 2058.90
E(Cash to investors)
Minus
Implied Equity Risk Premium (1/1/15) = 7.95% - 2.17% = 5.78%
Equals
100.5 growing @ 5.58% a year
2058.90 = 106.10(1+ r)
+112.91(1+ r)2
+118.26(1+ r)3
+124.85(1+ r)4
+131.81(1+ r)5
+131.81(1.0217)(r −.0217)(1+ r)5
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Implied Premiums in the US: 1960-‐2014
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0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
1960196119621963196419651966196719681969197019711972197319741975197619771978197919801981198219831984198519861987198819891990199119921993199419951996199719981999200020012002200320042005200620072008200920102011201220132014
Impl
ied
Prem
ium
Year
Implied Premium for US Equity Market: 1960-2014
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Implied Premium versus Risk Free Rate
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0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Implied ERP and Risk free Rates
Implied Premium (FCFE)
T. Bond Rate
Expected Return on Stocks = T.Bond Rate + Equity Risk Premium
Since 2008, the expected return on stocks has stagnated at about 8%, but the risk free rate has dropped dramatically.
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Equity Risk Premiums and Bond Default Spreads
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0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
ERP
/ Baa
Spr
ead
Pre
miu
m (
Sp
read
)
Figure 16: Equity Risk Premiums and Bond Default Spreads
ERP/Baa Spread Baa - T.Bond Rate ERP
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Equity Risk Premiums and Cap Rates (Real Estate)
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-‐8.00%
-‐6.00%
-‐4.00%
-‐2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Figure 17: Equity Risk Premiums, Cap Rates and Bond Spreads
ERP
Baa Spread
Cap Rate premium
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Why implied premiums maRer?
¨ In many investment banks, it is common pracWce (especially in corporate finance departments) to use historical risk premiums (and arithmeWc averages at that) as risk premiums to compute cost of equity. If all analysts in the department used the arithmeWc average premium (for stocks over T.Bills) for 1928-‐2014 of 8% to value stocks in January 2014, given the implied premium of 5.75%, what are they likely to find?
a. The values they obtain will be too low (most stocks will look overvalued)
b. The values they obtain will be too high (most stocks will look under valued)
c. There should be no systemaWc bias as long as they use the same premium to value all stocks.
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Which equity risk premium should you use?
If you assume this Premium to use
Premiums revert back to historical norms and your Wme period yields these norms
Historical risk premium
Market is correct in the aggregate or that your valuaWon should be market neutral
Current implied equity risk premium
Marker makes mistakes even in the aggregate but is correct over Wme
Average implied equity risk premium over Wme.
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And the approach can be extended to emerging markets Implied premium for the Sensex (September 2007)
¨ Inputs for the computaWon ¤ Sensex on 9/5/07 = 15446 ¤ Dividend yield on index = 3.05% ¤ Expected growth rate -‐ next 5 years = 14% ¤ Growth rate beyond year 5 = 6.76% (set equal to riskfree rate)
¨ Solving for the expected return:
¨ Expected return on stocks = 11.18% ¨ Implied equity risk premium for India = 11.18% -‐ 6.76% =
4.42% €
15446 =537.06(1+ r)
+612.25(1+ r)2
+697.86(1+ r)3
+795.67(1+ r)4
+907.07(1+ r)5
+907.07(1.0676)(r − .0676)(1+ r)5
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Can country risk premiums change? Brazil CRP & Total ERP from 2000 to 2013
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0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
2.50%3.51%
4.05%4.12%3.95%3.88%3.95%4.04%4.55%4.86%5.10%
7.64%
6.35%5.59%5.28%
4.06%3.15%
3.23%4.00%4.31%
3.70%
2.28%
0.82%
2.43%0.86%0.70%
0.69%
0.65%1.34%1.87%
Risk
Pre
miu
m
Figure 15: Implied Equity Risk Premium - Brazil
Brazil Country Risk
US premium
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The evoluWon of Emerging Market Risk
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Relative Risk MeasureHow risky is this asset, relative to the average
risk investment?
The CAPM BetaRegression beta of
stock returns at firm versus stock returns on market
index
Price Variance ModelStandard deviation, relative to the
average across all stocks
Accounting Earnings VolatilityHow volatile is your company's
earnings, relative to the average company's earnings?
Accounting Earnings BetaRegression beta of changes
in earnings at firm versus changes in earnings for
market index
Sector-average BetaAverage regression beta
across all companies in the business(es) that the firm
operates in.
Proxy measuresUse a proxy for risk (market cap, sector).
Debt cost basedEstimate cost of equity based upon cost of debt and relative
volatility
Balance Sheet RatiosRisk based upon balance
sheet ratios (debt ratio, working capital, cash, fixed assets) that measure risk
Implied Beta/ Cost of equityEstimate a cost of equity for firm or sector based upon price today and expected
cash flows in future
Composite Risk MeasuresUse a mix of quantitative (price,
ratios) & qualitative analysis (management quality) to
estimate relative risk
APM/ Multi-factor ModelsEstimate 'betas' against
multiple macro risk factors, using past price data
MPT Quadrant
Price based, Model Agnostic Quadrant
Accounting Risk Quadrant
Intrinsic Risk Quadrant
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Measuring Relative Risk
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The CAPM Beta
¨ The standard procedure for esWmaWng betas is to regress stock returns (Rj) against market returns (Rm) -‐ Rj = a + b Rm where a is the intercept and b is the slope of the regression.
¨ The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock.
¨ This beta has three problems: ¤ It has high standard error ¤ It reflects the firm’s business mix over the period of the regression, not the current mix
¤ It reflects the firm’s average financial leverage over the period rather than the current leverage.
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Beta EsWmaWon: The Noise Problem
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Beta EsWmaWon: The Index Effect
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Stock-‐priced based soluWons to the Regression Beta Problem
¨ Modify the regression beta by ¤ changing the index used to esWmate the beta ¤ adjusWng the regression beta esWmate, by bringing in informaWon
about the fundamentals of the company ¨ EsWmate the beta for the firm using
¤ the standard deviaWon in stock prices instead of a regression against an index
¤ RelaWve risk = Standard deviaWon in stock prices for investment/ Average standard deviaWon across all stocks
¨ EsWmate the beta for the firm from the boRom up without employing the regression technique. This will require ¤ understanding the business mix of the firm ¤ esWmaWng the financial leverage of the firm
¨ Imputed or implied beta (cost of equity) for the sector.
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AlternaWve measures of relaWve risk for equity
¨ AccounWng risk measures: To the extent that you don’t trust market-‐priced based measures of risk, you could compute relaWve risk measures based on ¤ AccounWng earnings volaWlity: Compute an accounWng beta or relaWve volaWlity ¤ Balance sheet raWos: You could compute a risk score based upon accounWng raWos
like debt raWos or cash holdings (akin to default risk scores like the Z score) ¨ Proxies: In a simpler version of proxy models, you can categorize firms
into risk classes based upon size, sectors or other characterisWcs. ¨ QualitaWve Risk Models: In these models, risk assessments are based at
least parWally on qualitaWve factors (quality of management). ¨ Debt based measures: You can esWmate a cost of equity, based upon an
observable costs of debt for the company. ¤ Cost of equity = Cost of debt * Scaling factor
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Determinants of Betas & RelaWve Risk
Beta of Firm (Unlevered Beta)
Beta of Equity (Levered Beta)
Nature of product or service offered by company:Other things remaining equal, the more discretionary the product or service, the higher the beta.
Operating Leverage (Fixed Costs as percent of total costs):Other things remaining equal the greater the proportion of the costs that are fixed, the higher the beta of the company.
Financial Leverage:Other things remaining equal, the greater the proportion of capital that a firm raises from debt,the higher its equity beta will be
Implications1. Cyclical companies should have higher betas than non-cyclical companies.2. Luxury goods firms should have higher betas than basic goods.3. High priced goods/service firms should have higher betas than low prices goods/services firms.4. Growth firms should have higher betas.
Implications1. Firms with high infrastructure needs and rigid cost structures should have higher betas than firms with flexible cost structures.2. Smaller firms should have higher betas than larger firms.3. Young firms should have higher betas than more mature firms.
ImplciationsHighly levered firms should have highe betas than firms with less debt.Equity Beta (Levered beta) = Unlev Beta (1 + (1- t) (Debt/Equity Ratio))
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