risk free rate and risk premium

Question 1

what instruments can you use to observe the real interest rate naturally? is the real rate equal in all countries?

Answer 1

you can use TIPS rate for all countries outside of those that have limitations on capital market imports and frictions. in that case real rf rate is equal to projected long term growth.

Question 2

what are the 2 ways of estimating ERP? what are the underlying assumptions?

Answer 2

historical averages (can predict the future) and implied ERP (the market is correclty priced)

Question 3

how do you pass from Ke-USD to Ke-LC

Answer 3

Ke-LC = (1+Ke-USD)· (1+inflation-LC)/ (1+inflation-USD) −1

Question 4

how do you apply the CRP to the Ke formula? what are underlying assumptions?

Answer 4

Ke=rf+B(ERP)+CRP if all firms of the country are equally exposed to CRP

Ke=rf+B(ERP+CRP) if exposure to CRP is similar to exposure to market risk (assuming country risk is a portion of market risk)

Ke=rf+B(ERP)+J(CRP) firm has a different exposure to CRP.

Question 5

what are the most important choices when estimating historical ERP?

Answer 5

time period: higher period introduces non-relevant data and survivorship bias but increases statistical precision–>tradeoff
which riskless security to use: be consistent with the choice for the risk free rate.
arithmetic or geometric average: depends if returns are serially correlated.

Question 6

what are the methods you can use to back out the risk free rate in a local currency whose emitting body does not sell any risk free assets (argentinian peso)?

Answer 6

1)Default spread approach
rf in Local Currency (LC) = Govt Bond rate (LC) − Default Spread

default spread can be obtained as the difference in rates if the country emits US dollar denominated bonds, using credit rating average default spread or CDS spread.

2) build up–> rf= expected inflation+expected real growth rate

3)derivative markets (use covered interest parity CIP instruments)–> CIP forward rate= CIP spot rate*((1+rf-local)/(1+rf-USD)). this method only works if the market is frictionless

4)uncovered interest parity in countries with frictions in capital markets–> (1+rf-USD)=(1+rf-local)*(1+expected inflation USD)/(1+expected inflation local)

Question 7

how can you calculate CRP?

Answer 7

1) default spread

2) relative standard deviation–> compute the ratio between the SD of the local market and that of the US market. ERP-local= ERP-US*relative SD, CRP=ERP-local - ERP-US.

3)hybrid–> compute ratio of SD between the local market and the country’s bonds. CRP= default spread*relative SD.

Question 8

what should be the maturity of the chosen risk free rate for valuation purposes?

Answer 8

the same as the asset being valued

Question 9

what is the formula for WACC

Answer 9

Kd(1-t)(D/D+E)+Ke*(E/D+E)

Question 10

what are issues when using relative SD to estimate CRP? possible solutions?

Answer 10

This approach presents the following shortcomings:
Stefano Rossi
a. Markets may have different structures and liquidity affecting volatility
b. There are risky emerging markets with low volatility driven by illiquidity
c. Currency differences between markets (USD vs local currency)
* Plausible solutions to the shortcomings:
a.-b. Examine carefully the market structure and its liquidity
c. Compute USD denominated returns when estimating volatility of market “X”

Question 11

what is the relationship between real and nominal rates?

Answer 11

real rate + exp.inflation = nominal rate for low rates of 1+real rate= (1+nominal rate)/(1+exp.inflatio) for higher rates

Question 12

how do you measure country risk exposure (lambda)?

Answer 12

Revenue breakdown
The easiest and most accessible data is on revenues, and most companies break their
revenues down by region. If so, can estimate λ as the proportion of a firm’s revenues
generated in a country and scale this to the proportion of domestic revenue generated by
the average firm in that country
λ firm,X =
2. Regression vs Country Bond
%ofrevenues in country Xfirm
%ofdomestic revenuesaveragefirmincountry X
Run regressions of stock returns for each firm against the returns of the country bond, for
the country X we want to estimate λ. The implicit assumption is that country bonds’
returns are a function of the country risk
re,firm
= α+λfirm,X ·rd,X +ε
λfirm,X = Cov(re,firm,rd,X)

Question 13

what are issues when using default spread to estimate CRP? possible solutions?

Answer 13

This approach presents the following shortcomings:
a. Ratings agencies seem to lag markets in responding to changes in CRP
b. Focus on default risk may obscure other risks that could affect equity markets
* Plausible solutions to the shortcomings:
Stefano Rossi
a. Use Credits Default Spreads (CDS) over a long time period (e.g. 10 year)
b. Use other measure of risk, such as (i) insurance prices (if available), (ii) country scores (The Economist)
c. Correct the default spreads by the relative standard deviation.