Question

According to CAPM, there is linear relationship between the assets but APT assumes linear relationship between the risk factors.

**APT**- Arbitrage Pricing Theory is a method of
estimating the price of the assets. This theory is based on
macroeconomics, market and security specific factors.

Formula- E(r_{j}) = r_{f} + b_{j1}
RP_{1} +b_{j2} RP_{2} + b_{j3}
RP_{3}.......

Where E(r_{j}) = Asset's expected rate of return,
r_{f} = risk free rate, b_{j} = the senstivity of
the asset's return to the factor, RP = the risk premium associated
with the factor.

**CAPM**- Capital Asset Pricing Model tells the
relationship between risk and expected return. It is used in
pricing of securities that are risky in nature. It says that the
expected return of a portfolio is equal to the risk free rate of
return and the risk premium.

Formula- r_{a} = r_{f} + Beta (r_{m} -
r_{f})

Where r_{a} = expected return, r_{f}
= risk free rate, r_{m} = expected market return.

I am not sure what is the exact risky factors here, meanwhile what is the asset in the CAPM model? Cheers

Answer #1

The risky factors here mean the factors that influence the change in expected return and the actual return. These include changes in market conditions, changes in the economy of a country, the financial results of the company and the like. These risks include systematic and unsystematic risks. Systematic risks are those that cannot be mitigated and have to be included while assessing return. Unsystematic risks those that can be reduced by diversification of a portfolio.

Assets in CAPM is to means the securities held in the portfolio of an investor i.e. stocks, bonds, T-bills among others.

Ms. Bessie, manager of Everchanging Mutual
Fund, know he fund currently is well diversified
and that it has a CAPM beta of 1.0. The risk-free
rate is 8% and the CAPM risk premium [E(Rm –
Rf] is 6.2%. She has recently become aware of
APT measures of risk and knows that there are
(at least) two factors: Industrial Production κ1
and inflation κ2. The equation for APT is
E(Ri) – Rf = [k1-Rf] bi1 + [k2-Rf] bi2
E(Ri) = 0.08...

Question 3
The following three factors have been identified as explaining a
stock’s returns and its sensitivity to each factor and the risk
premium associated with each factor is also calculated.
Gross Domestic Product (GDP) growth: = 0.5; RP = 3%
Inflation rate: = 0.7; RP = 3%
S&P’s 500 index return: = 1.4; RP = 8% The risk-free rate
is 4%
Using the asset pricing theory (APT) formula, calculate the
expected return. (4 points)

1)Consider the multifactor APT with two factors. The risk
premium on the factor 1 portfolio is 3%. The risk-free rate of
return is 6%. The risk-premium on factor 2 is 7.75%. Suppose that a
security A has an expected return of 18.4%, a beta of 1.4 on factor
1 and a beta of .8 on factor 2. Is there an arbitrage portfolio? If
not, prove it, if yes exhibit it?
2)In the APT model, what is the nonsystematic standard deviation...

The stock of Arbor Pet Trees (APT) is priced based on the given
systematic risk factors. Estimated sensitivities to these risk
factors are given by the betas of the regression
RAPT – Rrf =
βcreditRcredit + βvalue
Rvalue + α + ε
Factor
Risk Premium
Beta
Credit Risk
6.8%
1.1
Valuation Risk
3.7%
0.2
Risk-free rate
2%
What is the expected return on the stock of Arbor Pet Trees if
the stock is fairly valued?

According to the CAPM, the required return of an asset is the
sum of risk-free rate of return and beta times the risk
premium.
True
False

Discuss why is the relationship between expected return and
standard deviation for portfolios of risky and risk-free assets
linear

Consider the multifactor APT. There are two independent economic
factors, F1 and F2. The
risk-free rate of return is 6%. The following information is
available about two well-diversified portfolios:
Portfolio
ββ on F1
ββ on F2
Expected Return
A
1.0
2.0
19
%
B
2.0
0.0
12
%
Assuming no arbitrage opportunities exist, the risk premium on
the factor F1 portfolio should be

1. Select the correct answer. a. Stand-alone risk is the risk an
investor would face if he or she held portfolio of assets. b.
Risk-averse investors like risk and require lower rate of return as
an inducement to buy riskier securities. c. Risk premium is the
difference between the expected rate of return on a given risky
asset and that on a less risky asset. d. Capital Asset Pricing
Model is based on the proposition that any stock’s required rate...

Assume that you are in the two-factor exact APT world. There are
two portfolios (portfolio 1 and portfolio 2) which have loadings on
the two factors as follows:
Loadings
factor 1
factor 2
portfolio 1
1.5
0.55
portfolio 2
1.41
-1.1
The expected return on portfolio 1 is 8.04% and the expected
return on portfolio 2 is 14.09%. The risk-free rate is 2.1%.
There is a new portfolio just formed (portfolio 3). It has
loadings of 3 and 1.5 on...

1) The systematic risk of an investment:
A. is likely to be higher in a rising
market
B. results from its own unique factors
C. depends upon market volatility
D. cannot be reduced by diversification
2) Consider the CAPM. The risk-free rate is 5% and the
expected return on the market is 15%. What is the beta on a stock
with an expected return of 12%?
A. 0.5
B. 0.7
C. 1.2
D. 1.4
3) An asset with a negative...

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