CAPITAL MARKET EXPECTATIONS (2)

The Singer-Terhaar: First market imperfections: illiquidity

The ICAPM assumes perfect markets (markets w/out any frictional costs, where all assets trade in liquid markets). Thus, we need to add an estimated illiquidity premium to an ICAPM expected return estimate as appropriate

Grinold Kronner Equation

1. Exp. Income Return: D/P - Change in Shrs 2. Exp Nominal earnings growth rate: i + g 3. Exp. Repricing return: Change in PE

Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner (x) o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Analysts have frequently used the GGM form of the dividend discount model, solved for the required rate of return (r), to formulate the LONG TERM expected return of equity markets. The expected rate of return is composed of two parts: • the dividend yield (D1/P0) and • the capital gains (or appreciation) yield (g) The quantity g can be estimated most simply as the growth rate in nominal nominal GDP (sum of the estimated real growth rate in GDP + the expected LONG-RUM inflation rate) To account for diff. between the expected growth of the overall economy & specific company, analyst can use: Earning growth rate = GDP growth rate + Excess corp growth (can be positive or negative)

Singer and Terhaar 1. Estimate the risk premium of each asset: RP Brazilian equities = stand dev of asset x corr x SRmkt RP Brazilian bond= stand dev of asset x corr x SRmkt

Asset class's risk premium equals the product of the Sharpe ratio (RPM/σM) of the world market portfolio, the asset's own volatility, and the asset class's correlation with the world market portfolio: An asset class's risk premium is therefore the expected excess return accruing to the asset class given its global systematic risk (i.e., its beta relative to the world market portfolio).

Singer and Terhaar

Assuming that the risk premium on any currency equals zero—PPP holds—the ICAPM gives the exp. return on any asset as the sum of: • the (domestic) risk-free rate, and • risk premium based on the asset's sensitivity to the world market portfolio and expected return on the world market portfolio in excess of the risk-free rate. To summarize, to arrive at an expected return estimate using the Singer-Terhaar approach, we take the following steps: • Estimate the perfectly INTEGRATED and the completely SEGMENTED risk premiums for the asset class using the ICAPM. • Add the applicable ILLIQUIDITY premium, if any, to the estimates from the prior step. • Estimate the degree to which the asset market is perfectly integrated. • Take a weighted average of the perfectly integrated and the completely segmented risk premiums using the estimate of market integration from the prior step.

What is the formula for correlation between two assets: CORRa,b =

CORRa,b = Beta asset a x Beta asset b x (standard deviation of global markets)/stand dev of a x stand dev b

The Singer-Terhaar: Second market imperfections: Market Integration

Calculate the Risk Premium under perfect segmentation and perfect integration: Then use a weighted method to calculate the overall RP for asset i. Lastly, to estimate the Expected return on the asset: Exp Return = Rf + RP i

Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: (x) o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: o 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach (x) 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Financial equilibrium models describe relationships between EXPECTED RETURN and RISK in which SUPPLY and DEMAND are in balance. Equilibrium approaches to setting capital market expectations include: • Black-Litterman approach • International CAPM-based approach presented in Singer and Terhaar (1997) The Black-Litterman approach reverse-engineers the expected returns implicit in a diversified market portfolio, combining them with the investor's own views in a systematic way that takes account of the investor's confidence in his or her views. Singer and Terhaar (1997) proposed an equilibrium approach to developing capital market expectations that involves calculating the expected return on each asset class based on the international capital asset pricing model (ICAPM), taking account of market imperfections that are not considered by the ICAPM.

Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner (x) o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Grinold and Kroner (2002) provided a restatement of the Gordon growth model that takes explicit account of repurchases. Their model also provides a means for analysts to incorporate expectations of valuation levels through the familiar P/E ratio.

3.1. FORMAL TOOLS: Statistical Methods: o 3.1.1.1: Sample Estimators: (x) o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

If future returns over the selected time horizon reflect the same probability distribution as past returns (because the time series is STATIONARY—that is, the parameters that describe the return-generating process are unchanged), the resulting estimate will be useful. I.E: • the sample return (arithmetic or geometric) as an estimate of the expected return; • the sample variance as an estimate of the variance; • sample correlations as estimates of correlations. Choice between an arithmetic mean & a geometric mean: - AMR best represents mean return in a single period. - GMR of a sample represents the compound rate of growth that equates the beg value to the end of a data . - GMR represents multi-period growth MORE ACCURATELY than the AMR - GMR is ALWAYS LOWER than the arithmetic mean return for a risky variable. - The diff. between the AM and the GM in historical estimates of the equity risk premium can be substantial. Using a historical statistical approach for the equity risk premium and a current term-structure estimate for the expected return on bonds (e.g.,YTM on a zero-coupon government bond), the expected return on equities could be estimated as their sum

3.3. Judgment

In a disciplined expectations-setting process, the analyst should be able to factually explain the basis and rationale for forecasts. Quantitative models such as equilibrium models offer the prospect of providing a non-emotional, objective rationale for a forecast. The expectations-setting process nevertheless can give wide scope to applying judgment—in particular, economic and psychological insight—to improve forecasts. In forecasting, numbers, including those produced by elaborate quantitative models, must be evaluated.

3.2. Survey and Panel Methods

Involves asking a group of experts for their expectations and using the responses in capital market formulation. If the group queried and providing responses is fairly stable, the analyst in effect has a panel of experts and the approach can be called a PANEL METHOD. These approaches are based on the straightforward idea that a direct way to uncover a person's expectations is to ask the person what they are.

The Singer-Terhaar: Second market imperfections: Market Integration

Market integration means that there are no impediments or barriers to capital mobility across markets. Market integration implies that two assets in different markets with identical risk characteristics must have the same expected return. Market segmentation means that there are some meaningful impediments to capital movement across markets. When markets are segmented, two assets in different markets with identical risk characteristics may have different expected returns. If an asset in a segmented market appears undervalued to a nondomestic investor not considering barriers to capital mobility, after such barriers are considered, the investor may not actually be able to exploit the opportunity.

3.1. FORMAL TOOLS: Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Model that explains the returns to an asset in terms of the values of a set of return drivers or risk factors. Useful for modeling asset returns and covariances among asset returns. Multifactor models are useful for estimating covariances for the following reasons: 1. By relating the returns on all assets to a common set of return drivers, a multifactor model SIMPLIFIES the task of estimating covariances: estimates of covariances between asset returns can be derived using the assets' factor sensitivities. 2. When the factors are well chosen, a multifactor model approach may FILTER OUT NOISE (i.e., random variation in the data specific to the sample period). 3. Easy to verify the consistency of the covariance matrix, bc if the smaller factor covariance matrix is consistent, so are any covariances computed on the basis of it.

How to estimate the illiquidity premium

One approach uses the investment's multiperiod Sharpe ratio (MPSR): Based on the investment's multiperiod wealth in excess of the wealth generated by the risk-free investment (i.e., compounded return over compounded cash return). The relevant MPSR is one calculated over a holding period equal to the investment's lockup period. There would be no incentive to invest in an illiquid alternative investment unless its MPSR—its risk-adjusted wealth—were at least as high as the MPSR of the market portfolio at the end of the lockup period. Suppose that an alternative investment has a lockup period of 8yrs and its ICAPM-given required rate of return is 12% but its MPSR is below that of the GIM—say, 0.67—at an 8yr horizon. If increasing its expected return to 20% makes the alternative investment's MSPR equal 0.67 at the 8yr horizon, then the estimate of the illiquidity premium is 20% − 12% = 8%.

Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: (x) o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: o 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Risk Premium Approach: The risk premium approach expresses the expected return on a risky asset as the sum of the risk-free rate of interest and one or more risk premiums that compensate investors for the risky asset's exposure to sources of priced risk. The risk premium approach (sometimes called the BUILD UP APPROACH) is most often applied to estimating the required return in EQUITY and BOND markets.

3.1. FORMAL TOOLS: Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: (x) o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Shrinkage estimation involves taking a weighted average of a historical estimate of a parameter and some other parameter estimate, where the weights reflect the analyst's relative belief in the estimates. • The term "shrinkage" refers to the approach's ability to reduce the impact of extreme values in historical estimates. The procedure has been applied to COVARIANCES and MEAN RETURNS. Shrinkage estimator is a superior approach for estimating the population covariance matrix for the MEDIUM- and SMALLER-size DATASETS that are typical in finance.

The Risk Premium Approach: BUILD UP APPROACH 3.1.3.3. The Equity Risk Premium

The equity risk premium (ERP) is the compensation required by investors for the additional risk of equity compared with debt (debt has a prior claim on the cash flows of the company). "long-term" has usually been interpreted as 10 or 20 years. Equation 8 has been called the BOND YIELD PLUS RISK PREMIUM method of estimating the expected return on equity.

The Risk Premium Approach: BUILD UP APPROACH o 3.1.3.2: Fixed Income Premiums:

The expected bond return, E(Rb), can be built up as the real rate of interest plus a set of premiums: Expected Return on Bond = Real Risk Free Rate + 1. Inflation Premium 2. Default Risk Premium 3. Illiquidity Premium 4. Maturity Premium 5. Tax Premium

3.1. FORMAL TOOLS: Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: (x) o 3.1.1.4: Multifactor Models: Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

Time-series estimators involve forecasting a variable on the basis of lagged values of the variable being forecast and often lagged values of other selected variables. Useful in developing particularly SHORT TERM FORECASTS for FINANCIAL and ECONOMIC variables. Have been notably applied to ESTIMATING NEAR TERM VOLATILITY, given persuasive evidence of variance clustering (particularly at high frequencies, such as daily and weekly) in a number of different markets, including equity, currency, and futures markets. VOLATILITY CLUSTERING: Tendency for large (small) swings in prices to be followed by large (small) swings of random direction. Volatility clustering captures the idea that some markets represent periods of notably high or low volatility.

Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

• DCF models are a basic tool for establishing the intrinsic value of an asset based on fundamentals (e.g., its projected cash flows) and its fair required rate of return. • DCF models have the advantage of being forward-looking. • They do not address short-run factors such as current supply-and-demand conditions, so practitioners view them as more appropriate for setting long-term rather than short-term expectations. • That said, asset prices that are disconnected from fundamentals may reflect conditions of speculative excess that can reverse abruptly.

Statistical Methods: o 3.1.1.1: Sample Estimators: o 3.1.1.2: Shrinkage estimators: o 3.1.1.3: Time Series Estimators: o 3.1.1.4: Multifactor Models: (x) Discounted Cash Flow Models: o 3.1.2.1. Equity Markets: GGM & Grinold Kronner o 3.1.2.2: Fixed Income Markets: (x) The Risk Premium Approach: o 3.1.3.1: General Expression: o 3.1.3.2: Fixed Income Premiums: o 3.1.3.3: The Equity Risk Premium: 3.1.4:Financial Market Equilibrium Models: Singer-Terhaar Approach 3.2. SURVEY AND PANEL METHODS 3.3. JUDGMENTS:

• The DCF model is a standard tool in the pricing of fixed-income instruments. • Bonds are quoted in terms of the single discount rate (YTM) that equates the PV of the instrument's promised CFs to its market price. • The YTM of a reference instrument for a bond mkt segment is a readily available first approximation of the market expected return for the asset segment at a time horizon equal to the maturity of the instrument. • The YTM calculation makes the strong assumption that as interest payments are received, they can be reinvested at an IR that always equals the YTM. • Therefore, the YTM of a bond with intermediate cash flows is an estimate of the expected rate of return on the bond that is more or less plausible depending on the level of the YTM. • If a representative zero-coupon bond is available at the chosen time horizon, its YTM would be a superior estimate.