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Second Investment Course – November 2005

Topic One:

Expected Returns & Measuring the Risk Premium

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Some Important Concepts Involving Expected Investment Returns

1. Investors perform two functions for capital markets:- Commit Financial Capital- Assume Risk

so,

E(R) = (Risk-Free Rate) + (Risk Premium)

2. The expected return (i.e., E(R)) of an investment has a number of alternative names: e.g., discount rate, cost of capital, cost of equity, yield to maturity. It can also be expressed as:

k = (Nominal RF) + (Risk Premium)= [(Real RF) + E(Inflation)] + (Risk Premium)

where:

Risk Premium = f(business risk, liquidity risk, political risk, financial risk)

3. Investors can be compensated in two ways:- Period Cash Flows- Capital Gain

so,

E(R) = E(Cash Flow) + E(Capital Gain)

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Rt = (1 + Rft) (1+ RPt) – 1

or

Rt = (1 + Inft) (1 + RRft) (1 + RPt) – 1

where Rt = return on asset class for year t,

Inft = inflation rate

Rft = risk free rate

RRft = real risk free rate

RPt = risk premium

RPt =

where RRt = real asset class return

Measuring Expected Returns: Overview

Risk Premium

1 + Rft

1 + Rt - 1 =1 + RRft

1 + RRt - 1

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Developing Expected Return Assumptions With the Risk Premium Approach

March, 2005 18

T bills

Real Interest

Rate

Inflation

Term Premium

Credit Risk

Premium

T notes

CorpBonds

USEquities

Equity Risk

Premium

3.00%

1.00%

1.40%

1.25%

1.5% to 2.0%

4.00%

5.40%6.65%

8.15%to

8.65%T bills

Real Interest

Rate

Real Interest

Rate

InflationInflation

Term Premium

Term Premium

Credit Risk

Premium

Credit Risk

Premium

T notes

CorpBonds

USEquities

Equity Risk

Premium

Equity Risk

Premium

3.00%

1.00%

1.40%

1.25%

1.5% to 2.0%

4.00%

5.40%6.65%

8.15%to

8.65%

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Methods for Estimating the Equity Risk Premium

1. Historical Evidence

2. Fundamental Estimates

3. Economic Estimates

4. Surveys

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Estimating the Equity Risk Premium

1. Historical Evidence: Representative Work

– Ibbotson Associates – US Markets (2004)

– Fidelity Investments - Global Markets (2004)

– Jorion and Goetzmann (Journal of Finance, 1999)

– Siegel (Financial Analysts Journal, 1992)

– Dimson, Marsh and Staunton (Business Strategy Review, 2000)

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Ibbotson Associates U.S. Return & Risk Data: 1926 - 2004

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Historical Returns and Risk for Various U.S. Asset Classes

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Historical Global Stock Market Volatility

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More on Historical Asset Class Returns: U.S. Experience

Stocks:

Bonds:

T-Bills:

Inflation:

1926-2004: Avg. Return 12.39% 6.19% 3.76% 3.13% Std. Deviation 20.31% 8.56% 3.14% 4.32% 1980-2004: Avg. Return 14.73 11.05 6.09 3.75 Std. Deviation 16.33 11.51 3.26 2.43 1995-2004: Avg. Return 14.00 9.45 3.92 2.49 Std. Deviation 21.09 9.32

1.90 0.81

2000-2004: Avg. Return -0.70 9.92 2.72 2.60 Std. Deviation 20.32 5.04 2.10 0.97 Source: Ibbotson Associates

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Historical Risk Premia vs. T-bills: U.S. Experience

Stocks: Bonds:

Stock - Bond

Difference:

1926-2004: 8.63% 2.43% 6.20%

1980-2004: 8.64 4.96 3.68

1995-2004: 10.08 5.53 4.55

2000-2004: -3.42 7.20 -10.62

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Data for Historical Global Analysis

Series Starting Dates

Stocks Bonds Stocks Bonds

Argentina Jan-1988 May-1991 Italy Jan-1925 Jan-1862Australia Nov-1882 Jan-1859 Japan Jan-1921 Dec-1870Austria Jan-1970 Aug-1945 Mexico Jan-1970 Jan-1995Belgium Jan-1951 Jul-1832 Netherlands Jan-1951 Nov-1915Canada Jan-1934 Sep-1855 New Zealand Aug-1986 Mar-1925Chile Feb-1927 Jan-1993 Norway Jan-1970 Dec-1876Denmark Jan-1970 Jul-1821 Portugal Jan-1988 Jan-1976Finland Jan-1962 Jan-1960 South Africa Mar-1960 Dec-1860France Mar-1895 Mar-1800 Spain May-1940 Dec-1940Germany Jan-1870 Jan-1924 Sweden Jan-1919 Jan-1922Greece Jan-1977 n/a Switzerland Mar-1966 Mar-1915Ireland Jan-1988 Jun-1928 UK Oct-1694 Aug-1700Israel Jan-1993 Nov-1993 USA Mar-1871 Mar-1800

Source: Global Financial Data

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Historical Real Returns, 1954-2003: The Global Experience

Historical Real Returns, 1954-2003

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

Ann

ually

Com

poun

ded

Rea

l Ret

urn,

%

Equities

Bonds

Chile: Returns 1/54 – 6/03Chile*: Returns 1/54 – 12/71; 1/76 – 6/03Source: Global Financial Data

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Global Historical Volatility Measures, 1954-2003

Historical Risk, 1954-2003

0%

5%

10%

15%

20%

25%

30%

35%

40%

Ann

ually

Com

pou

nded

Rea

l Ret

urn,

%

Equities

Bonds

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Global Historical Risk Premia, 1954-2003

Risk Premia of Stocks and Bonds to Cash, 1954-2003

-2%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Ann

ually

Com

poun

ded

Rea

l Ret

urn,

%

Equities-CashBonds-Cash

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Estimating the Equity Risk Premium (cont.)

2. Fundamental Estimates: Representative Work

– Fama and French (University of Chicago, 2000)

– Ibbotson and Chen (Yale University, 2001)

– Claus and Thomas (Journal of Finance, 2001)

– Arnott and Bernstein (Financial Analysts Journal, 2002)

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Fundamental Risk Premium Estimates: An Overview

One potential problem with using historical averages to estimate future expected returns is that there is no way to control for the possibility that the past data sample you selected produced averages that are “abnormal” (i.e., too high or too low) in some way.

Another problem we have seen is that historical average returns tend to be fairly unstable (i.e., they are extremely sensitive to the time period chosen in the analysis).

Fundamental risk premium estimates attempt to objectively forecast the expected returns that would normally occur, given the fundamental relationships that tend to exist in the capital markets. In other words, fundamental forecasts attempt to link return expectations to the economic conditions likely to pertain in the market during the forecast interval.

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Fama and French: The Equity Risk Premium

Main Idea: Use dividend and earnings growth rates to measure the expected rate of capital gains for equity investments. This process creates two ways of then estimating real (i.e., inflation-adjusted) expected equity returns:a. E(R) = E(Div Yld) + E(Real Growth Rate of Dividends) = RDb. E(R) = E(Div Yld) + E(Real Growth Rate of Earnings) = RY

Notice that the intuition behind this approach is simply that it is possible to compensated investors in two ways: cash flow and capital gain.

Real Equity Risk Premium can then be estimated by subtracting short-term commercial paper yields from RD and RY, which leaves RXD and RXY, respectively.

Main Result: Using data from the period 1951 to 2000 for the US market (i.e., S&P 500), they find that:- RXD = 2.55%- RXY = 4.32%

Notice that both of these fundamental risk premium estimates are well below the average historical risk premium during the period (i.e., 7.43%), leading the authors that future expected returns to equity investments are unlikely to match the high levels of the recent past.

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Fama and French: The Equity Risk Premium (cont.)

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Claus and Thomas: Equity Risk Premia in US and International Markets

Main Idea: Based on the notion that the fundamental value of an equity investment can be described by its book value plus the present value of future abnormal earnings.

This valuation can be estimated by a modified version of the multi-stage growth model:

where the discount rate k (= rf + rp) is the equity expected return.

Main Results: Using observed market data (e.g., p, bv) and analyst forecasts (e.g., g) for the other inputs over 1985-1998, the authors calculate the values of the equity risk premium (rp) that solve the model:

- US: 3.40%- Japan: 0.21%- UK: 2.81%- France: 2.60%- Canada: 2.23%

1t

t00

rp) rf (1

)gae(1 bv p

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Claus and Thomas: Estimates of Equity Risk Premia for US Markets

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Arnott and Bernstein: What Risk Premium is “Normal”?

Main Idea: The risk premium for stocks relative to bonds can be forecast as the difference between the expected real stock return and the expected real bond return

The real return to stocks consists of three components:- Dividend yield- Growth rate in the real dividend- Change in equity valuation level (e.g., change in market P/E)

The real return to bonds consists of three components:- Nominal yeld- Inflation- Change in yield times duration (i.e., reinvestment)

Main Conclusions: - Historical real stock returns and the excess return for stocks relative to bonds

over the past century have extraordinarily high (due to rising valuation multiples) and unlikely to be repeated in the future. The fundamental expected risk premium estimate over this past period would have been 2.4%.

- Future expectations should be based on tractable fundamental relationships and indicate a real risk premium of near 0%.

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Arnott and Bernstein: What Risk Premium is “Normal”? (cont.)

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Estimating the Equity Risk Premium (cont.)

3. Economic Estimates: Representative Work

– Black and Litterman (1992)

– Asset Class-Specific Risk Premia

– Ennis Knupp Associates (2005)

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Implied Returns and the Black-Litterman Forecasting Process

The Black-Litterman (BL) model uses a quantitative technique known as reverse optimization to determine the implied returns for a series of asset classes that comprise the investment universe.

The main insight of the BL model is that if the global capital markets are in equilibrium, then the prevailing market capitalizations of these asset classes suggest the investment weights of an efficient portfolio with the highest Sharpe Ratio (i.e., risk premium per unit of risk) possible.

These investment weights can then be used, along with information about asset class standard deviations and correlations, to transform the user’s forecast of the global risk premium into asset class-specific risk premia (and expected returns) that are consistent with a capital market that is in equilibrium.

These equilibrium expected returns for the asset classes can then be used as inputs in a mean-variance portfolio optimization process or adjusted further given the user’s tactical views on asset class performance.

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The Black-Litterman Process: An Example

Consider an investable universe consisting of the following five asset classes:

- US Bonds- Global Bonds-ex US- US Equity- Global Equity-ex US- Emerging Market Equity

As of September 2005, these asset classes had the following market capitalizations (in USD millions):

- US Bonds $ 8,607,149 (17.71%)

- Global Bonds-ex US 12,426,562 (25.57%)- US Equity 13,776,249 (28.35%)- Global Equity-ex US 12,266,988 (25.24%)- Emerging Market Equity 1,521,275 ( 3.13%)

Total: $48,598,223

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Black-Litterman Example (cont.)

Consider also the following historical return standard deviations (October 2000 – September 2005):

usb = 4.02% gb = 8.81% uss = 15.62%

gs = 15.35% ems = 21.29%

The historical correlation matrix, measured using all available pairwise historical return data:

usb,gb = 0.41 gb,gs = 0.21

usb,uss = -0.14 gb,ems = -0.00

usb,gs = -0.16 uss,gs = 0.65

usb,ems = -0.20 uss,ems = 0.69

gb,uss = -0.02 gs,ems = 0.73

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Black-Litterman Example (cont.)

The remaining inputs that the user must specify are: (i) the global risk premium of the investment universe, and (ii) the risk-free rate. Using current market data we have:

- Global Risk Premium: 3.55% (10-yr Global Balanced)

- Risk-Free Rate: 4.30% (10-yr US Treasury)

The heart of the BL process is to then calculate the implied excess return for each asset class, using the following (stylized) formula:

[Risk Aversion Parameter] x [Covariance Matrix] x [Market Cap Weight Vector]

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Black-Litterman Example (cont.)

The risk aversion parameter is the rate at which more return is required as compensation for more risk. It is calculated as:

RAP = [Global Risk Premium] / [Market Portfolio Variance]

It can be shown in this example that the market portfolio variance is (8.57%)2 = 0.734%, so that:

RAP = (0.0355)/(0.0073) = 4.84

The covariance between two asset classes (Y and Z) is given by the formula:

Cov(Y,Z) = y,z x y x z

For instance, the covariance between US Equity and Global Equity-ex US is: (15.62%) x (15.35%) x (0.65) = 0.016

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Black-Litterman Example (cont.)

The implied excess return (IER) for US Equity can then be computed as follows:

IERuss = (RAP) x {[Cov(uss,usb) x wusb] + [Cov(uss,gb) x wgb] +

… + [Cov(uss,ems) x wems]}

= (4.84) x {(-0.001)(.1771) + … + (0.023)(.0313)} = 5.49%

More formally, the solution for the entire asset class implied excess return vector is given by:

0.05% 0.002 0.001 -0.001 -0.001 -0.002 17.71% 1.39% 0.001 0.008 0.000 0.003 0.000 25.57% 5.49% = (4.84) x -0.001 0.000 0.024 0.016 0.023 x 28.35% 5.64% -0.001 0.003 0.016 0.024 0.024 25.24% 6.59% -0.002 0.000 0.023 0.024 0.045 3.13%

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Black-Litterman Example (cont.)

The total expected return for US Equity is then simply the IER plus the risk-free rate:

4.30% + 5.49% = 9.79%

The excess and total expected returns for the other asset classes in this example are:

Excess Total

- US Bonds: 0.05% 4.35%- Global Bonds: 1.39% 5.69%- Global Equity: 5.64% 9.94%- Emerging Equity: 6.59% 10.89%

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Black-Litterman Example: Excel Spreadsheet

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Black-Litterman Example: Proprietary Software (Zephyr Associates)

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Ennis Knupp Associates (EKA) – July 2005

EKA uses a similar process to the BL methodology in that they develop asset class expected return forecasts that are grounded in the notion that the global capital markets are in equilibrium.

Specifically, EKA estimates asset class expected returns to be consistent with a global Capital Asset Pricing Model (CAPM). Two expected return “anchors” are used as a starting point:

- US Equity = 9.1%: Total return is divided into three components: dividend yield (1.7%), nominal growth rate of corporate earnings (7.4%), and change in valuation levels (0%)

- US Bonds = 5.4%: Based on two components: current yield and simulated future changes in yields (based on forecasts of expected inflation, inflation risk premium, and real yields)

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EKA Fundamental Expected Return Estimates (cont.)

Other asset class expected returns are then estimated relative to these anchors using the global CAPM. Specifically, expected returns on the various asset classes are proportional to their systematic risk levels relative to the global market portfolio, shown at the right.

For example, the ratio of the US Bonds beta (0.40) to the US Equity beta (1.71) is 0.23. This implies that the ratio of US Bond risk premium to US Equity risk premium should also be 23%.

Therefore:

(5.4 – RF)/(9.1 – RF) = 0.23

which results in an implied risk-free rate of 4.3%. The risk premium of each asset class is then calculated so that it is directly proportional to its systematic risk, given these two anchors

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EKA Fundamental Expected Return Estimates (cont.)

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Estimating the Equity Risk Premium (cont.)

4. Surveys: Representative Work

– Graham and Harvey (Duke University, 2005)

– UTIMCO (2005)

– Ennis Knupp: Managers & Consultants (2005)

– Burr (Pensions and Investments, 1998)

– Welch (Journal of Business, 2000)

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Campbell-Harvey Survey of Corporate CFOs – June 2005

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Survey of Asset Class Return & Risk Expectations:UTIMCO Staff & External Expert Opinions – March 2005

March, 2005 20

Asset CategoryCambridge Associates

Goldman Sachs

Wilshire Associates

BridgeWater BGIEnnisKnupp

10 yearsCitigroup

Consultant Average

HistoricalUTIMCO

2003UTIMCO

2005

US Equity Nominal Returns 10.00% 8.00% 9.20% 7.90% 8.06% 8.80% 10.00% 8.85% 11.53% 8.50% 8.50% Real Returns 7.00% 5.80% 6.95% 5.00% 6.06% 6.30% 7.50% 6.37% 6.86% 5.50% 5.50% Std Deviation 17.00% 17.30% 17.00% 15.50% 15.50% 17.00% 15.79% 16.44% 15.82% 17.00% 17.00%

Global Equity Nominal Returns 10.00% 7.70% 9.75% 7.60% 8.06% NA 10.00% 8.85% 11.86% 8.50% 8.50% Real Returns 7.00% 5.50% 7.50% 4.70% 6.06% NA 7.50% 6.38% 7.19% 5.50% 5.50% Std Deviation 20.00% 17.40% 20.00% 14.50% 16.25% 19.00% 15.23% 17.48% 16.77% 19.00% 19.00%

Emerging Markets Equity Nominal Returns 13.00% 8.30% 11.40% 9.30% 9.14% NA 10.90% 10.34% 15.04% 11.00% 10.50% Real Returns 10.00% 6.10% 9.15% 6.40% 7.14% NA 8.40% 7.86% 10.36% 8.00% 7.50% Std Deviation 28.00% 23.60% 27.00% 21.00% 25.00% NA 24.22% 24.80% 23.25% 26.00% 26.00%

Absolute Return Hedge Funds Nominal Returns 7.00% 8.40% 6.82% NA NA NA 5.40% 6.91% 10.79% 7.00% 7.00% Real Returns 4.00% 6.20% 4.57% NA NA NA 2.90% 4.42% 6.12% 4.00% 4.00% Std Deviation 9.00% 4.90% 8.00% NA NA NA 4.06% 6.49% 6.15% 7.50% 7.50%

Directional Hedge Funds Nominal Returns 9.00% 8.40% 6.82% NA NA NA 9.60% 8.46% 10.48% 8.00% 8.00% Real Returns 6.00% 6.20% 4.57% NA NA NA 7.10% 5.97% 5.81% 5.00% 5.00% Std Deviation 13.00% 4.90% 8.00% NA NA NA 7.56% 8.37% 8.16% 11.00% 10.00%

Venture Capital Nominal Returns 15.00% NA 15.25% 10.30% NA NA 16.40% 14.24% 15.16% 14.00% 14.00% Real Returns 12.00% NA 12.99% 7.40% NA NA 13.90% 11.57% 10.49% 11.00% 11.00% Std Deviation 28.00% NA 30.00% 25.00% NA NA 43.50% 31.63% 18.78% 30.00% 30.00%

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Survey of Asset Class Return & Risk Expectations (cont.):UTIMCO Staff & External Expert Opinions – March 2005

March, 2005 21

Asset CategoryCambridge Associates

Goldman Sachs

Wilshire Associates

BridgeWater BGIEnnisKnupp

10 yearsCitigroup

Consultant Average

HistoricalUTIMCO

2003UTIMCO

2005

Private Equity Nominal Returns 13.00% 10.70% 15.25% 10.30% 10.00% NA NA 11.85% 11.32% 11.50% 11.50% Real Returns 10.00% 8.50% 12.99% 7.40% 8.00% NA NA 9.38% 6.65% 8.50% 8.50% Std Deviation 24.00% 29.10% 30.00% 25.00% 30.00% 31.40% NA 28.25% 9.04% 20.00% 24.00%

REITs Nominal Returns 9.00% 5.60% 8.78% 7.50% 6.45% NA 10.00% 7.89% 14.54% 7.50% 7.50% Real Returns 6.00% 3.40% 6.52% 4.60% 4.45% NA 7.50% 5.41% 9.87% 4.50% 4.50% Std Deviation 15.00% 13.90% 16.00% 14.00% 13.20% 11.50% 11.87% 13.64% 14.74% 15.00% 15.00%

Commodities (Financial) Nominal Returns 8.00% 4.50% NA 6.70% NA NA NA 6.40% 13.37% 5.00% 6.00% Real Returns 5.00% 2.30% NA 3.80% NA NA NA 3.70% 8.70% 2.00% 3.00% Std Deviation 19.00% 18.40% NA 18.00% NA NA NA 18.47% 18.43% 18.00% 18.00%

TIPS Nominal Returns 5.50% NA 4.43% 5.50% 4.34% NA NA 4.94% 9.07% 5.50% 5.50% Real Returns 2.50% NA 2.17% 2.60% 2.34% NA NA 2.40% 4.39% 2.50% 2.50% Std Deviation 6.00% NA 6.00% 6.00% 6.00% NA NA 6.00% 3.69% 6.00% 6.00%

Fixed Income Nominal Returns 6.00% 4.60% 4.63% 5.30% 4.86% 5.80% 5.10% 5.18% 8.80% 5.00% 5.75% Real Returns 3.00% 2.40% 2.37% 2.40% 2.86% 3.30% 2.60% 2.70% 4.13% 2.00% 2.75% Std Deviation 7.00% 4.50% 5.00% 5.00% 5.50% 6.40% 4.00% 5.34% 6.02% 6.00% 7.00%

Cash Nominal Returns 4.00% 2.70% 2.75% 4.00% 3.05% NA 3.50% 3.33% 6.43% 4.00% 4.00% Real Returns 1.00% 0.50% 0.50% 1.10% 1.05% NA 1.00% 0.86% 1.75% 1.00% 1.00% Std Deviation 2.00% 0.00% 1.00% 0.30% 1.50% NA 0.46% 0.88% 0.91% 1.00% 1.00%

Inflation Returns 3.00% 2.20% 2.25% 2.90% 2.00% 2.50% 2.50% 2.48% 4.67% 3.00% 3.00% Std Deviation NA NA NA 1.50% 1.00% NA NA 1.25% 1.17% 2.00% 1.50%

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Ennis Knupp Associates Survey – Spring 2005