• Although use of long time series data increases the precision* of estimates of population parameters and reduces the sensitivity of parameter estimates to the starting and ending dates
Trang 1Reading 16 Capital Market Expectations
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Capital market expectations (CME) (also known as
macro expectations) represent the investors’
expectations regarding the risk and return prospects of
broad asset classes They help investors in formulating
their strategic asset allocation, that is, in setting rational
return expectations on a long term basis for globally
diversified portfolios
By contrast, micro expectations represent the investors’
expectations regarding the risk and return prospects of individual assets They facilitate investors in security selection and valuation
2 ORGANIZING THE TASK: FRAMEWORK AND CHALLENGES
2.1 A Framework for Developing Capital Market
Expectations
A framework for developing Capital market
expectations has the following seven steps
1 Specify the final set of expectations that are needed,
including the investment time horizon: This step
involves clearly specifying the questions that need to
be answered
• An investor/analyst must determine the specific
objectives of the analysis E.g for a taxable investor,
the objective is to develop long-term after-tax
capital market expectations
• An investor/analyst must specify the relevant set of
asset classes (consistent with the investment
constraints) on which the investor/analyst needs to
develop capital market expectations
• It is important to understand that the scope of the
capital market expectations-setting framework is
directly related with the number and variety of
permissible asset class alternatives i.e the greater
the number and variety of permissible asset classes,
the wider the scope of setting capital market
expectations Refer to Example 1 on page 9
NOTE:
If the number of asset classes is n, the analyst will need to
estimate:
• n number of expected returns;
• n number of standard deviations;
• (n2 – n) / 2 distinct correlations (or the same number
of distinct covariances);
2 Research the historical record: Historical data provide
some useful information on the investment
characteristics of the asset Hence, the historical
performance of the asset classes should be analyzed
in order to identify their return drivers Analyzing each
asset class’s historical performance involves gathering
macroeconomic and market information in different
ways e.g., by:
• Geographical area (e.g., domestic, nondomestic, or
some subset e.g a single international area); or
• Broad asset class (e.g equity, fixed-income, or real estate); or
• Economic sector/industry/sub-industry basis;
The historical data can be used as a baseline and may
be adjusted for analyst’s views e.g if an analyst is optimistic (pessimistic) relative to the consensus on the prospects for asset class A, then he/she may make an upward (downward) adjustment to the historical mean return
3 Specify the method(s) and/or model(s) that will be used to formulate CME and the information required
to develop such models:
• The analyst should clearly specify the method(s) and/or model(s) that will be used to develop CME
• The method(s) and/or model(s) used must be consistent with the objectives of the analysis and investment time horizon e.g a DCF method is most appropriate to use for developing long-term equity market forecasts
4 Determine the best sources for the information needed: The analysts/investors should search for the best and most relevant sources for the information needed and should be constantly aware of new, superior sources for their data needs It involves considering following factors:
• Data collection principles and definitions;
• Error rates in collection and calculation formulas;
• Quality of asset class indices (i.e Investability, correction for free float, turnover in index constituents);
• Biases in the data;
• Costs of data etc;
In addition, the analysts must select the appropriate data frequency e.g long-term data series should be used for setting long-term expectations or evaluating long-term volatility In general,
• For setting long-term CME, quarterly or annual data series are useful
Trang 2• For setting shorter-term CME, daily data series are
useful
5 Interpret the current investment environment: The
analyst should interpret the current investment
environment using the selected data and methods
and should employ consistent set of assumptions
Also, he should apply experience and judgment
(where necessary to interpret any conflicting
information within the data) so that the conclusions
are mutually consistent
6 Provide the set of expectations that are needed and
document conclusions: This step involves
documenting answers to the questions formulated in
step 1 In addition to answers and conclusions, the
analyst should also document reasoning and
assumptions associated with the conclusion The set of
expectations obtained in step 6 are then used to
develop forward-looking forecasts on capital markets
7 Monitor actual outcomes to provide feedback to
improve the CME development process: This step
involves monitoring and comparing actual outcomes
against expected outcomes to identify weaknesses in
the CME development process so that the
expectations-setting process or methods can be
improved
Beta versus Alpha Research:
Beta Research: Beta research involves developing
capital market expectations concerning the systematic
risk and returns to systematic risk Unlike alpha research,
beta research is centralized which implies that CME
inputs used across all equity and fixed-income products
are consistent
Alpha Research: Alpha research involves developing
expectations regarding individual assets in an attempt to
capture excess risk-adjusting returns by a particular
investment strategy
Three Characteristics of Good Forecasts: Good forecasts
are
1) Unbiased, objective, and well researched;
2) Efficient i.e has minimum forecasting errors;
3) Internally consistent i.e if asset class A and B are
perfectly negatively correlated and asset class B and
C are also perfectly negatively correlated, then asset
class A and C must be perfectly positively correlated
2.2 Challenges in Forecasting (section 2.2.1 - 2.2.9)
The data and assumptions used in the forecasting model must be error free The challenges associated with forecasting include:
1) Limitations of Economic Data:
• Definitions and calculation methods may change over time This may affect the validity of time-series data
• Errors in collection and measurements of data and in the calculation formulas;
• Timeliness of data i.e time lag with which economic data are collected, processed, and disseminated For example, the International Monetary Fund sometimes provides macroeconomic data for developing economies with a lag of two years or more
o The greater the lag before information is reported (i.e the older the data), the greater the risk that it provides irrelevant and uncertain information about the present situation
• Changes in the construction method of data: The bases of indices of economic and financial data are changed on a periodic basis to reflect more current bases This process is known as re-basing Re-basing simply reflects a mathematical change rather than substantive change in the composition of an index Re-basing may result in risk of mixing data indexed to different bases
2) Data Measurement Errors and Biases: The errors and biases in data measurement include:
Transcription errors: The errors relating to gathering and recording of data are called transcription errors Transcription errors are most serious when they reflect bias
Survivorship bias: Survivorship bias occurs when a data series reflects data on surviving (or successful) entities and do not reflect post-delisting data (e.g data on entities with poor performance which have been removed from the database) This bias results in overestimated historical returns
Appraisal (smoothed) data: Infrequently traded and illiquid assets (e.g real estate, private equity etc) do not tend to have up-to-date market prices; rather, their values need to be estimated, known as appraised values Appraised values (i.e smoothed data) represent less volatile values As a result, the correlations of such assets with traditional assets (i.e equities and fixed income) and risk (S.D.) of assets are underestimated or biased downward
• Remedy to mitigate smoothing effect: The smoothed data bias can be mitigated by rescaling the data so that their dispersion (i.e S.D.) is increased but the mean of the data is unchanged
Practice: Example 4 & 5,
Volume 3, Reading 16
Trang 33) The Limitations of Historical Estimates: The simplest
approach to forecasting is to use historical data to
directly forecast future outcomes However, the
historical estimates may not be good predictors of
future results because the risk/return characteristics of
asset classes may change as a result of changes in
technological, political, legal and regulatory
environments and disruptions i.e war or natural
disaster These so called regime changes introduce
the statistical problem of non-stationarity (where
different parts of a data series exhibit different
underlying statistical properties) In addition, the
disruptions in a certain time period may temporarily
increase volatilities in that period which may not be
relevant for the future period
• Although use of long time series data increases the
precision* of estimates of population parameters
and reduces the sensitivity of parameter estimates to
the starting and ending dates of the sample;
however, using long time series (reflecting multiple
regimes) may increase the risk of non-stationarity in
the data (due to structural changes during the time
frame) and consequently, the risk of including
irrelevant data
• In addition, for some time-series analysis, the data
series of the required length may not be available
Using high-frequency data (weekly or even daily) in
order to get data series of required length increases
risk of asynchronism (i.e discrepancy in the dating of
observations due to use of stale/out-of-date data)
and results in underestimated correlations estimates
*Precision of the estimate of the population mean is
proportional to 1 / √number of observations
4) Ex Post Risk Can Be a Biased Measure of Ex Ante Risk:
In general, the ex-ante risk and ex-ante return are
underestimated on backward-looking basis Hence,
ex-post risk estimates may be a poor proxy of the ex
ante risk estimate The investment decision-making
must be based on ex-ante risk measures rather than
ex-post risk measures
5) Biases in Analysts’ Methods
Data-mining bias: Data mining bias refers to over-using
or overanalyzing the same or related data (i.e mining
the data) until some statistically significant pattern is
found in the dataset Two signs that may indicate the
existence of data-mining bias include:
i Many of the variables used in the research are not
reported;
ii No plausible economic relationship exists among
variables;
The data mining bias can be detected by using
out-of-sample data to test the statistical significance of the
patterns found in the dataset
Time-period bias: Time-period bias occurs when
outcomes/results are time-period specific For example,
a short time series may give period-specific results that may not reflect a longer time period Similarly, test based
on long time period may suffer from structural changes occurring during the time frame, resulting in two data sets with different relationships As a result, forecasted relationship estimated from the first period may not hold for second sub-period
6) The Failure to Account for Conditioning Information may lead to misperceptions of risk, return, and risk-adjusted return: Future risk and return of an asset as of today depend or are conditional upon on specific characteristics of the current marketplace and prospects looking forward Hence, the expectations concerning future risk and return of an asset must take into account any new, relevant information in the present For example, since systematic risk of an asset class varies with business cycle, the expectations concerning systematic risk of an asset class should be conditioned upon the state of the economy
7) Misinterpretation of Correlations: A significantly high correlation between variable A and B implies one of the following things:
• Variable A is predicted by variable B i.e variable B is
exogenous variable (which is determined outside
the system) and variable A is endogenous variable
(which is determined within the system)
• Variable B is predicted by variable A i.e variable A is exogenous variable and variable B is endogenous variable
• Neither variable A predicts B nor B predicts A; rather,
a third variable C predicts A and B the variable C is
referred to as a control variable
Suppose,
• Beta of an asset class in economic expansions = 0.80
• Beta of an asset class in economic recessions = 1.2
• Expected return on market during expansion = 12%
• Expected return on market during recession = 4%
• Risk-free rate (both recession & expansion) = 2%
Unconditional beta = 0.50 (0.80) + 0.50 (1.2) = 1.0 Unconditional risk-free rate = 0.50 (2%) + 0.50 (2%) = 2%
Unconditional expected return on market = 0.50 (12%) + 0.5 (4%) = 8%
Unconditional expected return on asset class i (using CAPM) = 2% + 1.0 (8% - 2%) = 8%
Expected return on market during expansion (using CAPM) = 2% + 0.80 (12% - 2%) = 10%
Expected return on market during recession (using CAPM) = 2% + 1.20 (4% - 2%) = 4.4%
Conditional expected return on market = 0.50 (10%) + 0.50 (4.4%) = 7.2%
Unconditional alpha = 7.2% - 8% = -0.8%
Alpha during expansion and recession = 0.50 (0%) + 0.50 (0%) = 0%
EXAMPLE
Trang 4The impact of multiple control variables can be
analyzed using multiple-regression analysis
Multiple-regression analysis A = β0 + β1 B + β2 C + ε
• The coefficient β1 represents the partial correlation
between A and B i.e the effect of variable B on
variable A after taking into account the effect of the
control variable C on A
• The coefficient β2 represents the partial correlation
between A and C i.e the effect of variable C on
variable A after taking into account the effect of
variable B on A
• When estimated value of β1 is significantly different
from 0 but β2 is not significantly different from 0, it
indicates that variable B predicts variable A
Time series analysis A = β0 + β1 Lagged values of A + β2
Lagged values of B + β2 Lagged values of C + ε NOTE:
It must be stressed that two variables may reflect low or
zero correlation despite strong but non-linear relationship
because correlation measure ignores non-linear
relationships
8) Psychological Traps
Psychological traps can undermine the analyst’s ability
to make accurate and unbiased forecasts
a) The anchoring trap: It is a tendency of people to
develop estimates for different categories based on a
particular and often irrelevant value (both
quantitative & qualitative), called anchor (i.e a
target price, the purchase price of a stock, prior
beliefs on economic states of countries or on
companies etc) and then adjusting their final
decisions up or down based on that “anchor” value
• Anchoring bias implies investor under-reaction to
new information and assigning greater weight to the
anchor
• Anchoring bias can be mitigated by avoiding
premature conclusions
b) The status quo trap: It is a tendency of people to
prefer to “do nothing” (i.e maintain the “status quo”)
instead of making a change In the status-quo bias,
investors prefer to hold the existing investments in their
portfolios even if currently they are not consistent with
their risk/return objectives
• It is closely related with avoiding “Error of
commission” (i.e regret from an action taken) and
“Error of omission” (i.e regret from not taking an
action)
• The status-quo trap can be overcome by following a
rational analysis in investment decision-making
c) The confirming evidence trap: It is a tendency of people to seek and focus on information that confirms their beliefs or hypothesis and ignore, reject
or discount information that contradicts their beliefs Confirmation bias implies assigning greater weight to information that supports one’s beliefs This bias can
be reduced or mitigated by:
• Collecting and examining complete information i.e both positive and negative
• Actively looking for contradictory information and contra-arguments
• Being honest with one’s motives and investment objectives
d) The overconfidence trap: It is a tendency of people to overestimate their knowledge levels and their ability
to process and access information In this bias, people tend to believe that they have superior knowledge and they make precise and accurate forecasts than
it really is
• The overconfidence trap may result in using too narrow range of possibilities or scenarios in forecasting
• The overconfidence trap can be avoided by widening the range of possibilities around the primary target forecast
e) The prudence trap: It is the tendency of analysts to be extremely cautious in forecasting in an attempt to avoid making any extreme forecasts which may adversely impact their career As a result, they make forecast estimates that are in line with other analysts (representing herding behavior)
• The prudence trap can be avoided by widening the range of possibilities around the target forecast
f) The recallability trap: It is the tendency of analysts to assign higher weight to more easily available and easily recalled information e.g information related to catastrophic or dramatic past events This bias can be avoided by using objective data and procedures in decision-making
9) Model Uncertainty: Investment analysis may be subject to two kinds of uncertainty i.e
i Model uncertainty is the uncertainty related to the accuracy of the model selected The model uncertainty can be evaluated by analyzing the variation in outcomes of the models from shifting between the several most promising models Practice: Example 11,
Volume 3, Reading 16
Trang 5ii Input uncertainty is the uncertainty related to the
accuracy of inputs used in the model
Capital market anomalies (inefficiencies) often exist due
to input and model uncertainty
3 TOOLS FOR FORMULATING CAPITAL MARKET EXPECTATIONS
3.1 Formal Tools (Section 3.1.1 – 3.1.4)
Formal tools used for formulating capital market
expectations include:
I Statistical methods
II Discounted cash flow models
III The risk premium approach
IV Financial market equilibrium models
1 Statistical Methods: There are two major types of
Statistical methods
• Descriptive Statistics: Statistical Methods that are
used to organize and summarize data so that
important aspects of a dataset can be described
are known as descriptive statistics
• Inferential Statistics: Statistical Methods that are used
to make estimates or forecasts about a larger group
(population) based upon information taken from a
smaller group (sample) are known as inferential
statistics
a) Historical Statistical Approach: Sample Estimators: In a
historical statistical approach, historical data is used
as the basis for forecasts
• A sample estimator is a formula used to compute an
estimate of a population parameter The value of
that estimate (statistic) is called a point estimate
• The point estimate is useful to estimate population
parameter when the time series data is stationary
• In a mean-variance framework, the analyst might
use:
o The sample arithmetic mean of total return or
sample geometric mean of total return as an
estimate of the expected return The arithmetic
mean is appropriate to use to estimate the mean
return in a single period whereas the geometric
mean is appropriate to use to estimate mean
return for multi-periods For a risky (volatile)
variable, the geometric mean return will always be
< the arithmetic mean return
o The sample variance as an estimate of the
variance; and
o Sample correlation as an estimate of correlation
b) Shrinkage Estimators: Shrinkage estimation is a
process in which an estimate of a parameter is
computed by taking weighted average of a historical
estimate of a parameter and some other estimate of
a parameter Shrinkage estimation is also known as
the “two-estimates-are-better-than-one” approach
Shrinkage Estimator = (Weight of historical estimate ×
Historical parameter estimate) + (Weight of Target parameter estimate × Target parameter estimate)
For example, Shrinkage estimator of the covariance matrix = (Weight
of historical covariance × Historical covariance) + (Weight of Target covariance × Target covariance) Where,
Target parameter estimate = Alternative parameter
estimate
• The target covariance matrix can be a model-based estimate or can be a covariance estimate based on the assumption that each pair-wise covariance is equal to the overall average covariance
factor-• Weights reflect the analyst’s relative belief in the estimates e.g the more strongly an analyst believes
in the historical estimate, the larger the weight of the historical estimate
• The historical sample covariance matrix is not appropriate to use for small samples Hence, shrinkage estimation is a superior approach for estimating population parameter for the medium and smaller size because it helps to decrease (i.e shrink) the impact of extreme values in historical estimates and increases the efficiency of the parameter estimates The more plausible target estimate is selected, the greater the improvement in the accuracy of the estimate
• The Shrinkage estimation method is commonly used for computing covariances and mean returns Example:
• Weight of historical estimate = 0.30
• Weight of target estimate = 0.70 Shrinkage estimate of the covariance = 0.70 (40) + 0.30
(75) = 50.5
Trang 6c) Time-Series Estimators: Time series estimation involves
regressing the value of dependent variable on the
lagged values of dependent variable and lagged
values of other selected variables Time series
estimation methods are useful to make short-term/
near-term forecasts for financial and economic
variables They are also used to forecast near-term
volatility, assuming variance clustering exists
• Variance clustering: When large (small) fluctuations
in prices are followed by large (small) fluctuations in
prices in random direction, it is referred to as
“Variance Clustering”
σ2t = βσ2t-1 + (1 – β) ε2t Where,
σ2t = Volatility in period t
σ2t-1 = Volatility in previous period
ε2t = a random “noise” term
β = Weight on σ2t-1 Measure of rate of decay of
the influence of the value of volatility in period
t-1 on value of volatility in period t with 0
<β< 1
o The higher (lower) the β, the greater (smaller) the
influence of the value of volatility in period t-1 on
value of volatility in period t
d) Multifactor Models: A multifactor model involves
regressing the value of dependent variable on values
of a set of return drivers or risk factors It can be stated
• Markets’ factor sensitivities (bik), also known as factor
betas or factor loadings, measure the responsiveness
of markets to factor movements
εi = An error term that represents the asset’s
idiosyncratic or residual risk i.e portion of the return
to asset i not explained by the factor model
• It is assumed that an error has mean value of zero
and is uncorrelated with each of the K factors and
with the error terms in the equations for other assets
Uses of Multifactor models for estimating covariances: 1) A multifactor model simplifies the method of estimating covariances because the estimates of covariances between asset returns can be computed from the assets’ factor sensitivities
2) A multifactor model helps to filter out noise (i.e random fluctuations in the data specific to the sample period) provided that appropriate risk factors are selected
3) A multifactor model simplifies verification of the consistency of the covariance matrix because when the smaller factor covariance matrix is consistent then any covariances estimated using smaller factor covariance matrix is also consistent
Example:
Suppose that returns of all assets in the investable universe depend on two factors*:
1 Global equity factor
• Standard deviation of global equity = 12% Variance for global equity = (0.12)2 = 0.0144
2 Global bond factor
• Standard deviation of global bonds = 5% Variance for global bonds = (0.05)2 = 0.0025
• Correlation between global equity and global bonds = 0.30
Covariance between global equity and global bonds = S.D of Global equity × S.D of Global bonds × Correlation between Global equity & Global bonds =
12% × 5% × 0.30 = 0.0018 Equity-bond covariance matrix
Global Equity Global Bonds
Equity
Global Bonds
Residual Risk (%)
• The zero sensitivity of Market A to global bonds does not imply that Market A has zero correlation with global bonds; rather, it implies that the partial correlation (i.e correlation after removing impact of the other markets) of Market A with global bonds is Practice: Example 12,
Volume 3, Reading 16
Trang 7zero Hence, return in Market A is not derived by
Covariance of market i with market j can be computed
using following formula:
Mij = bi1 bj1 Var (F1) + bi2 bj2Var (F2) + (bi1 bj2 + bi2 bj1)
Cov (F1, F2)
For i = 1 to n, j = 1 to n, and i ≠ j
Computing Covariance between Markets A and B: with i
= 1 for Market A and j = 2 for Market B:
M12 = (1.11) (1.07) (0.0144) + (0) (0) (0.0025) + [(1.11) (0) +
(0) (1.07)] (0.0018) = 0.01710288
*A multi-factor approach can also be used depending
on investors/analysts needs
2 Discounted Cash Flow Models: In Discounted cash
flow models (DCF models), an asset’s intrinsic value is
computed as the present value of its (expected) cash
flows It is a forward-looking model and is most
appropriate to use for making long-term forecasts
Where,
V0 = Value of the asset at time t = 0 (today)
CFt = Cash flow (or the expected cash flow, for risky
cash flows) at time t
r = Discount rate or required rate of return Assuming
flat term structure, the discount rate will be the
same for all time periods
3.1.2.1 Equity Markets
Gordon growth model: The Gordon growth model is
preferred to use for developed economies in setting
long-run expectations It can be expressed as:
P
D g P
g D
+
= + +
0 1 0
= Dividend Yield + Capital gains Yield
Where,
E (Re) = the expected rate of return on equity
D0 = Most recent annual dividend per share
g = Long-term growth rate in dividends, assumed
equal to the long-term earnings growth rate;
P0 = Current share price
• The growth rate (g) can be estimated as the growth rate in nominal GDP
Nominal GDP = Real growth rate in GDP + Expected
long-run inflation rate Earnings growth rate = Nominal GDP growth rate +
Excess Corporate growth (for the index companies*)
*Excess corporate growth reflects adjustment for any differences between economy’s growth rate and that of equity index E.g for a broad-based equity index, the excess corporate growth adjustment, if any, should be small
Grinold-Kroner Model: It is a restatement of the Gordon growth model and it explicitly takes into account the impact of number of shares in the market (as
represented by stock repurchases)and changes in market valuations as represented by the price to earnings (P/E) ratio It is expressed as follows:
E (Re) ≈ ࡰࡼ - ∆S + i + g + ∆PE Where,
E (Re) = Expected rate of return on equity D/P = Expected dividend yield
∆S = Expected % change in number of shares
outstanding this term is negative (i.e -∆S) when there are net positive share repurchases;
∆S is positive when number of shares outstanding increases
-∆S = Positive repurchase yield +∆S = Negative repurchase yield
i = Expected inflation rate
g = Expected real total earnings growth rate (generally, it is not identical to EPS growth rate, with changes in shares outstanding)*
∆PE = Per period % change in the P/E multiple
*GDP Growth rate = Labor productivity growth + Labor
supply growth Where, labor supply growth = Population growth rate + Labor force participation growth rate
Sources of Expected rate of return on equity: The expected rate of return on equity can be decomposed
as follows:
1) Expected income return = D/P - ∆S 2) Expected nominal earnings growth return = i + g 3) Expected repricing return = ∆PEP/E tends to increase when investors expect stocks to be less risky
in future It is considered as the most volatile source of total return
4) Expected Capital gains return = Expected nominal earnings growth rate + Expected repricing return
Trang 8Example: Suppose the analyst estimates a 2% dividend
yield, long term inflation of 3.2%, earnings growth rate of
4.5%, a repurchase yield of -0.5% and P/E re-pricing
return of 0.35%
Expected return on the stock = 2.0% + 3.2% + 4.5% - 0.5%
+ 0.35% = 9.55%
Fed Model: According to the Fed model, stock market is
overvalued (undervalued) when the market’s current
earnings yield < (>) 10-year Treasury bond yield The
earnings yield is a conservative estimate of the
expected return for equities because it is the required
rate of return for no-growth equities For details, refer to
Reading 18
3.1.2.2 Fixed-Income Markets
Bonds are quoted in terms of a single discount rate,
referred to as yield to maturity or YTM YTM is the
discount rate that equates the present value of the
bond’s promised cash flows to its market price
• Typically, YTM of a reference fixed-income security
(called bellwether) is used as a proxy for expected
rate of return on the bond
• YTM is a superior estimate for expected rate of return
on the zero-coupon bond (i.e bond with no
intermediate cash flows) because it assumes that as
interest payments are received, they can be
reinvested at an interest rate equal to YTM
• For callable bonds, yield-to-worst is sometimes used
as a conservative estimate of expected rate of
return
3 The Risk Premium Approach: In the risk premium
approach, the expected return on a risky asset “i” is
computed as follows
E (Ri) = RF + (Risk premium)1 + (Risk premium)2 + …+ (Risk
premium) K
Where,
E(Ri) = Asset’s expected return
RF = Risk-free rate of interest
NOTE:
When assets are fairly priced, an asset’s required return =
Investor’s expected return
3.1.3.2 Fixed-Income Premiums
The expected bond return, E (Rb), can be estimated as
follows:
E(Rb) = Real risk-free interest rate + Inflation premium +
Default risk premium + Illiquidity premium +
Maturity premium + Tax premium
Where, a) Real risk-free interest rate is the single-period interest rate for a completely risk-free security if no inflation were expected It represents the compensation demanded by investors for forgoing current consumption
• The current real rate depends on cyclical factors
• The long-term real rate depends on sustainable equilibrium conditions
b) Inflation premium represents the compensation demanded by investors for risk associated with increase in inflation It is typically a more volatile component of bond yield
Inflation premium = Average inflation rate expected
over the maturity of the debt + Premium (or discount) for the probability attached to higher inflation than expected (or greater disinflation)
Or
Inflation premium = Yield of conventional government
bonds (at a given maturity) – Yield
on Inflation-indexed bonds of the same maturity
• Inflation premium varies depending on base currency consumption baskets
c) Default risk premium represents the compensation demanded by investors for the risk of default of the borrower
Default risk premium = Expected default loss in yield
terms + Premium for the diversifiable risk of default d) Illiquidity premium represents the compensation demanded by investors for the risk of loss associated with converting assets (particularly illiquid assets) into cash quickly The illiquidity premium is positively related to the illiquidity horizon e.g the longer the length of investment’s lock-up period for an alternative investment, the greater the illiquidity premium
non-e) Maturity premium represents the compensation demanded by investors for higher interest rate risk associated with longer-maturity debt
Maturity premium = Interest rate on longer-maturity,
liquid Treasury debt - Interest rate on short-term Treasury debt
f) A tax premium represents the compensation demanded by investors for assuming risk of lower after-tax return due to higher tax rates
Practice: Example 13 &14,
Volume 3, Reading 16
Trang 93.1.3.3 The Equity Risk Premium
The equity risk premium is the compensation demanded
by investors for assuming greater risk associated with
equity relative to debt
Equity risk premium = Expected return on equity (e.g
expected return on the S&P 500) – YTM on a long-term government bond (e.g 10-year U.S Treasury bond return)
Thus,
Expected return on equity = YTM on a long-term
government bond + Equity risk premium
• It is known as Bond-yield-plus-risk-premium method
4 Financial Market Equilibrium Models
Financial equilibrium models explain relationships
between expected return and risk when financial market
is in equilibrium (i.e where supply is equal to demand)
Types of Financial Market Equilibrium Models:
Black-Litterman approach: The Black-Litterman
approach determines the equilibrium returns using a
reverse optimization method i.e “reverse engineering”
them from their market capitalization in relation to the
market portfolio It then incorporates investor’s own
views in determining asset allocations For example, in
the absence of any investors’ views about a particular
asset class, market implied returns are used because its
equilibrium and optimal weights are identical
The international CAPM-based approach (ICAPM):
Under ICAPM, the
Expected return on any asset = Domestic risk-free rate +
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
Or
E (Ri) = RF +βi [E (RM) – RF]
Where,
E(Ri) = The expected return on asset i given its beta
RF = Domestic Risk-free rate of return
E(RM) = the expected return on the world market
portfolio
βi = the asset’s sensitivity to returns on the world
market portfolio, = Cov (Ri, RM) / Var (RM)
Assumptions of ICAPM: Purchasing power parity
relationship holds, implying that the risk premium on any
currency equals zero
World market portfolio: The global investable market
(GIM) can be used as a proxy for the world market portfolio GIM consists of traditional and alternative asset classes with sufficient capacity to absorb meaningful investment
An asset class risk premium (RPi) = Sharpe ratio of the world market portfolio × Asset’s own volatility × Asset class’s correlation with the world market portfolio
RPi = (RPM / σM) × σi × ρi,M Where,
RPM = Expected excess return
σM = Standard deviation of the world market portfoliorepresents systematic or non-diversifiable risk
• Market integration: International markets are integrated when there are no impediments or barriers to capital mobility across markets When markets are integrated, two identical assets with the same risk characteristics must have the same expected return across the markets
at different exchange rate adjusted prices in different countries, violating the law of one price)
o The more the market is segmented, the more it is dominated by local investors;
• In practice, the asset markets are neither perfectly segmented nor perfectly integrated In other words,
an asset market is partially segmented or integrated
Trang 10In summary: Steps of estimating Expected Return using
Singer-Terhaar Approach
1 Separately estimate the risk premium for the asset
class using the ICAPM under two cases i.e a perfectly
integrated market and the completely segmented
market
• When a market is completely segmented, the
reference market portfolio is the same as the
individual local market Consequently, the ρi,M = 1
Risk premium for a perfectly segmented market = RPi
RP
σ
σ
• The risk premium for a perfectly segmented market is
greater than that for the perfectly integrated
markets, all else equal
•Note: For simplicity, it is assumed that the Sharpe
ratio of the GIM is equal to the Sharpe ratio of the
local market portfolio
2 Add the applicable illiquidity premium, if any, to the
ICAPM expected return estimates (from step 1)
3 Estimate the degree of integration of the given asset
market For example, it has been observed that
developed market bonds & equities are approx 80%
integrated and 20% segmented
4 Estimate the risk premium assuming partial
segmentation by taking a weighted average of risk
premium under perfectly integrated markets and risk
premium under perfectly segmented markets The
weights represent degree of integration of the given
asset market (from step 3)
Risk premium of the asset class, assuming partial
segmentation = (Degree of integration × Risk premium
under perfectly integrated markets) + ({1 - Degree of
integration} × Risk premium under perfectly segmented
markets)
5 Estimate the expected return on the asset class by
adding the risk premium estimate (from step 4) to the
risk-free rate yields
Example:
Suppose
• S.D of Canadian bonds = 8%
• S.D of Canadian equities = 16%
• Correlation of Canadian bonds with GIM = 0.45
• Correlation of Canadian equities with GIM = 0.65
Step 3: The degree of integration is estimated to be 80%
or 0.80
Step 4: Final risk premium estimates are as follows Risk Premium (fixed income) = (0.80 × 1.008%) + (0.20 × 2.24%) = 1.2544%
Risk Premium (equities) = (0.80 × 2.912%) + (0.20 × 4.48%) = 3.2256%
Step 5: Expected return on bonds or equities = Risk-free rate + relevant risk premium
Expected return on bonds = 5% + 1.2544%
= 6.2544%
Expected return on equities = 5% + 3.2256%
= 8.2256%
Estimating the amount of illiquidity premium: The amount
of illiquidity premium of an asset can be estimated using investment’s multi-period Sharpe ratio (MPSR) MPSR reflects investment’s multi-period return in excess of the return generated by the risk-free investment adjusted for risk The MPSR must be calculated over the holding period equal to lock-up period of investment
Rule: The investor should invest in illiquid investment if it’s MPSR at the end of the lockup period ≥ MPSR of the market portfolio
Illiquidity premium = Expected return of an illiquid asset – Required rate of return on an illiquid asset at which its Sharpe ratio is equal to that of market’s Sharpe ratio Covariance between any two assets = Asset 1 beta × Asset 2 beta × Variance of the market
Trang 113.2 Survey and Panel Methods
In the Survey method of capital market expectations
setting, the analysts inquire a group of experts for their
expectations and then use their responses in formulating
capital market expectations When a group of experts
provide fairly stable responses, the group is referred to as
a panel of experts and the method is called a panel
method The limitation of survey method is that the
output from such surveys largely depends on the professional identity of the respondent
In a disciplined expectations-setting process, all the assumptions and rationales used in the analysis must be explicitly documented by an analyst In addition, the analyst must explicitly mention the judgments used in the analysis in an attempt to improve forecasts The process
of applying judgment can be formalized using a set of devices e.g checklists
According to the Asset-pricing theory, the risk premium
of an asset is positively correlated with its expected
payoffs in a given economic condition For example,
assets with high expected payoffs during periods of
weak consumption (business cycle troughs) tend to
have lower risk premiums (implying higher prices)
compared to assets with low expected payoffs during
such periods
An analyst who has greater ability to predict a change
in trend or point of inflection in economy activity and
who has the ability to identify economic variables
relevant to the current economic environment is
considered to have a competitive advantage The
inflection points are indicators of both unique investment
opportunities and source of latent risk
Two major Components of Economic Growth:
1) Trend Growth: It identifies the long-term component of
growth in an economy It is relevant for setting
long-term return expectations for asset classes
2) Cyclical Growth: It measures short-term fluctuations in
an economy Cyclical variation affects such variables
as corporate profits and interest rates etc
4.1 Business Cycle Analysis
There are two types of cycles associated with business
• It is important to note that the duration and
amplitude of each phase of the cycle, as well as the
duration of the cycle as a whole are sensitive to
major shocks in the economy (i.e wars, petroleum or
financial crisis, and shifts in government policy) and
vary considerably; hence, they are difficult to forecast
The economic activity can be measured using the following measures:
Gross domestic product (GDP): GDP represents the total value of final goods and services produced in the economy during a given year
GDP (using expenditure approach) =Consumption + Investment + Change in Inventories + Government spending + (Exports - Imports)
• Economists prefer to focus on Real GDP (i.e increase
in the value of GDP adjusted for changes in prices) because it reflects the change in the standard of living The higher the real GDP, the greater the standard of living
Output gap:
Output Gap = Potential value of GDP (i.e potential
output achieved if economy follows its trend growth) – Actual value of GDP
• The output gap is positive (i.e potential GDP > actual GDP) during period of economic recession or slow growth Inflation tends to fall when output gap
It is important to understand that real time estimates of output gap may not necessarily always be accurate because economy’s trend path is affected by changes
in demographics and technology
Practice: Example 18 &19,
Volume 3, Reading 16
Trang 12Recession: A recession refers to a broad-based
economic downturn i.e when an economy faces two
successive quarterly declines in GDP
4.1.1) The Inventory Cycle The inventory cycle is a cycle that identifies fluctuations
in inventories The inventory cycle results from adjusting
inventories at desired levels in response to changes in
expected level of sales
Phases of Inventory Cycle:
A Up phase: Future sales are expected to increase
leading to increase in production in an attempt to
increase inventories overtime pay and
employment increases to meet increasing production
needs as a result, economy boosts and sales further
increase
B Down phase: After reaching some peak point
(referred to as inflection point), sales start falling
and/or future sales are expected to fall (e.g due to
tight monetary policy, higher oil prices etc.)
Consequently, production is cut back and inventory
level decreases Due to reduction in production
layoffs, increase and/or hiring process slows down As
a result, economy slows down and sales further
decrease
• Generally, after an inflection point, the inventory
levels are adjusted to their desired levels within a
period of year or two
Indicator of Inventory Position: The inventory position can
be gauged using “Inventory/sales ratio” It is interpreted
as follows:
• Falling inventory/sales ratio indicates that in the near
future, businesses will try to rebuild inventory; as a
result, economy is expected to strengthen in the
next few years
• Sharply rising inventory/sales ratio indicates that in
the near future, businesses will try to reduce
inventory; as a result, economy is expected to
weaken in the next few years
It is important to understand that due to improved
techniques, i.e “just-in-time” inventory management,
inventory/sales ratio has been trending down
4.1.2) The Business Cycle The business cycle represents short-run fluctuations in
GDP (i.e level of economic activity) around its long-term
trend growth path A typical business cycle is comprised
of the following five phases:
1 Initial Recovery: The economy starts to grow from its
slowdown or recession This phase lasts for few
months
• Confidence among businesses starts to increase;
• Unemployment is still high → thus, consumer
confidence is at low levels;
• Inflation falls;
• Output gap is still large & there is spare capacity;
• The recovery largely results from the simultaneous upswing in the inventory cycle;
Economic Policies:
• Stimulatory monetary policy i.e interest rates fall;
• Stimulatory fiscal policy i.e budgetary deficit grows; Capital Market Effects:
• Government bond yields continue to fall in expectation of falling inflation and then start bottoming;
• Stock markets may perform well (i.e stock prices rise);
• Confidence among businesses is increasing;
• Unemployment starts to fall as more workers are hired in response to increased production & higher demand → consumer confidence starts rising → as
a result, consumers borrow more and spending increases;
• Inflation falls;
• Output gap is still large & there is spare capacity;
• The recovery largely results from the simultaneous upswing in the inventory cycle;
• Inventory levels build up in anticipation of future increase in sales;
• Capacity utilization increases → per unit cost falls → profits rise rapidly;
Economic Policies:
• Central bank starts withdrawing stimulatory monetary & fiscal policies introduced during recession;
Capital Market Effects:
• Short-term interest rates start rising;
• Longer-term bond yields may be stable or increase slightly;
• Stock markets are rising;