what is beta?
systematic risk of a security (non diversifiable)
from the perspective of the CAPM, it represents the correct measure of the risk of a security included in a diversified portfolio
foundations of the CAPM
- EFFICIENT FRONTIER
- investors only care about risk and return
- efficient portfolios generate the highest return for a given level of risk
- the possible combinations of ALL risky ASSETS is represented by the investment opportunity set
- in an economy without risky assets, RATIONAL investors only select portfolios that fall along the efficient frontier
- CAPITAL MARKET LINE (CML)
- when risk free rate is introduced, investors are more flexible to improve risk/return profile by borrowing and lending at the risk free rate (borrowing/lending allows investors to extend the CML beyond or before the risk return of the market portfolio to meet specific risk/return preferences)
- RATIONAL investors can purchase an ideal portfolio (market portfolio) and allocate funds across BOTH the ideal RISKY PORTFOLIO and RISK FREE assets
- the market portfolio is the point of tangency between the CML and the highest shape ratio (ideally, it would represent all risky assets in the economy but in reality people use stock indexes)
- !!! since all individuals portfolio combinations on the CML, by definition, have a correlation coefficient of 1 with the market and are perfectly diversified
- SECURITY MARKET LINE
- the SML is at the basis of the capital asset pricing model
- for a single security, considering its correlation wrt the market is no longer equal to 1, its expected return can be computed as:
E(r_i) = r_free + B*(r_mkt - r_free)
what is one disadvantage of operating EXCLUSIVELY on the efficient frontier?
not having investment opportunities below a certain risk
how to choose the “market portfolio” using CML
the market portfolio shows the highest SHARPE RATIO (slope of the CML):
[E(r_m) - R_free] / Std_m
why is the CML a straight line? Give an analytical example
because the standard deviation grows linearly with the % of market portfolio invested in the total portfolio
the return of the portfolio = risk_free + MRP * %invested in the market portfolio
examples of portfolios with different risk/return profile (visualize the CML)
slide 11
(from left to right)
1. all risk free
2. part in risk free part in risky
3. all in risky
4. all in risky and partly financed with debt
!!! “all” refers to the starting position, the available funds ad time 0
what is the beta coefficient of a security?
B_i = (Std_i / Std_mkt) * corr(i,mkt
or
B_i = Std_i / Std_mkt^2
where Std_i is basically the covariance between the return of the stock and the market
how can you determine if a security is “out of line” with respect to the CML?
above: undervaluation, return is excessive compared to its systematic risk
under: overvaluation, return is too low compared to its systematic risk
an efficient market will drive them anyways to the CML
how can we analytically estimate beta?
- using the formulas
cov(i,mkt) / std_mkt ^2
or
corr(i,mkt) * std_i / std_mkt
- calculating the regression coefficient beta of the regression
R_i = alpha_i + B_i * r_mkt
what is total beta?
there is an argument that investors in the market, ESPECIALLY for UNLISTED companies, are not perfectly diversified and therefore need to account for both systematic and idiosyncratic risk
the risk premium required is HIGHER than what emerges from the traditional CAPM
TOTAL B = std_i / std_mkt
what is higher between unlevered beta and total beta?
total beta
what are the 7 steps to practically estimate cost of capital k_e?
- choose the parameters of the analysis
a. returns (w/m)
b. time horizon (2,3,5 y)
c. reference mkt index (eurostoxx, S&P) - record asset price and value of the index for the period
- convert PRICES into RETURNS
r = (P1/P0) - 1 - calculate beta
a. determination of variables (formulas)
or
b. regression line - estimate MRP
- record risk free rate
- compute k_e
which are the 4 different approaches to ERP/MRP?
what are pros and cons of historical vs implicit/expected MRP?
A)
- default spread method/relative standard deviation: benchmarks the MRP of a country like the USA to that of the country to be estimated
- historical method: average stock market return of a **FINANCIALLY ADVANCED country **over a VERY LONG period
- panel of ** judgements**: trusts academics/auditors/investment banks
- market implied ERP
B)
historical
PROS:
- objective
CONS:
- maybe inconsistent with current/expected r_mkt
- you need reliable data
implicit
PROS:
- consistent with current and forward looking
CONS:
- hard to determine
- partly subjective
- conditioned by analysis quality
when do you use adjusted beta?
blume adjustment
cases when raw beta is particularly low or high
the rationale is that betas have a structural tendency towards 1 (mean reversion)
B_adj = 2/3* b_raw + 1/3 b_mkt
where b_mkt is obviously 1
what influences a company’s beta (anwer in qualitative terms)
- revenue cyclicality (positive)
- operating leverage (positive), the ratio between %change in operating income and %change in revenues
- financial leverage (positive), charges associated with debt are FIXED financial costs and this affects the relative variability of flows to equity
what is a particular case in which evaluating equity beta cannot leverage market returns?
- when the company is not listed (use comparables)
- when LISTED but there are low levels of capitalization or liquidity that could DISTORT available data (use comparables)
what are the 10 steps to determine the cost of corporate capital using industry beta?
- identify comparables
- compute beta equity of sample companies
- DELEVER beta equity
- average (or median) beta ASSET
- determine market financial structure
- RELEVER beta asset with respect to TARGET financial structure to obtain beta EQUITY of target
- calculate k_e
8a. value company’s equity on the basis of FCFE
…………………………………………………………………
8b. estimate k_d
- determine WACC according to chosen financial structure and tax rate
- find EV, then subtract financial debts net of liquidity
in beta computation, how do you neutralize the effect of financial structure, determining a parameter that expresses only the operating (systematic) risk relating to the different companies?
unlevered beta
formula slide 41
what influences equity beta (in quantitative terms)?
- difference between asset beta and debt beta
- degree of leverage of the firm !!!! at market values !!!!
- tax rate
does the firm’s financial leverage influence asset beta?
NO
asset beta is, by definition, unlevered and independent of the financial structure
does beta debt depend on financial leverage?
NO
also, it is constant and generally assumed between 0.2 and 0.23
what do we mean by industry beta?
the UNLEVERED arithmetic mean (or median) of a universe of comparables, with the exclusion of any outliers
relevering formula
slide 43
what changes when using damodaran’s simplifying relevering/unlevering formula?
beta debt is assumed to be 0
