ch.13 Flashcards
Expected returns
Expected returns are based on the probabilities of possible outcomes. In this context, “expected” means average if the process is repeated many times
The risk-return trade-off for a portfolio is measured by _______________________________________
the portfolio expected return and standard deviation, just as with individual assets.
A portfolio is
is a collection of assets
The expected return of a portfolio is
the weighted average of the expected returns for each asset in the portfolio
If two stocks are perfectly positively correlated, then there is simply a _______________ between the two securities
risk-return trade-off
Feasible set/ opportunity set
the curve that comprises all of the possible portfolio combinations.
Efficient set
the portion of the feasible set that only includes the efficient portfolio (where the maximum return is achieved for a given level of risk, or where the minimum risk is accepted for a given level of return).
Minimum Variance Portfolio
the possible portfolio with the least amount of risk.
Over time, the average of he _________ component is zero
unexpected
Is it the surprise or the expected component that affects a stock’s price therefore its return?
The surprise component
What are efficient markets?
Efficient markets are a result of investors trading on the unexpected portion of announcements. Efficient markets are a result of investors trading on the unexpected portion of announcements
systematic risk also known as
as non-diversifiable risk or market risk. Risk factors that affect a large number of assets. Includes such things as changes in GDP, inflation, interest rates, etc.
Unsystematic Risk, also known as
Also known as unique risk and asset-specific risk.
Risk factors that affect a limited number of assets
Includes such things as labor strikes, shortages, etc.
Total Return
expected return + systematic return+unsystematic return
Unexpected return =
systematic return + unsystematic return
Diversification
Portfolio diversification is the investment in several different asset classes or sectors.
Diversification is not just holding a lot of assets
Explain the principle of diversification
Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns.
This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another.
However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion.
Diversifiable (unsystematic) Risk
The risk that can be eliminated by combining assets into a portfolio.
Synonymous with unsystematic, unique or asset-specific risk.
If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away.
The market will not compensate investors for assuming unnecessary risk.
Total risk =
systematic risk +unsystematic risk
The standard deviation of returns is _________________________.
is a measure of total risk.
For well diversified portfolios, unsystematic risk is very __________.
Consequently, the total risk for a diversified portfolio is essentially equivalent
very small to the systematic risk.
Systematic Risk Principle
There is a reward for bearing risk.
There is not a reward for bearing risk unnecessarily.
The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away. Market will not compensate for bearing unsystematic risk.
When measuring systematic risk, a beta of 1 implies…
implies the asset has the same systematic risk as the overall market
When measuring systematic risk, a beta < 1 implies
the asset has less systematic risk than the overall market
When measuring systematic risk, a beta > 1 implies
the asset has more systematic risk than the overall market
Risk premium =
expected return- risk-free rate
The higher the beta, the _____ the risk premium
greater
slide 43
The slope of SML (security market line) is the ____
reward-to-risk ratio
What is the portfolio beta if 75% of your money is invested in the market
portfolio, and the remainder is invested in a risk-free asset?
By definition, the market portfolio has beta of 1 and risk-free asset has beta of
0. Therefore, the portfolio beta is given by 0.75 × 1 + 0.25 × 0 = 0.75.
Qs 1 Tutorial 13
Stock A has the expected return of
10% × 60% + 80% × 30% + 10% × 0% = 30%.
Stock B has the expected return of
10% × 40% + 80% × 30% + 10% × (−10%) = 27%.
Therefore, Stock A has higher expected return than B by 3%
The market has an expected rate of return of 9.8%. Long-term government
bonds are expected to yield 4.5% and Treasury bills are expected to yield 3.4%.
The inflation rate is 3.1%. What is the market risk premium?
We use the return of investing in treasury bills as the definition of risk-free rate.
Therefore, the market risk premium is expected return of the market minus the
T-bill rates = 9.8% − 3.4% = 6.4%
The stock of Martin Industries has a beta of 1.43. The risk-free rate of return
is 3.6% and the market risk premium is 9%. What is the expected rate of
return on Martin Industries stock?
Recall the CAPM equation: E[R] = Rf + β × MRP. Plugging in the
corresponding values, we have E[R] = 3.6% + 1.43 × 9% = 16.47%.
- What are the portfolio weights for a portfolio that has 135 shares of Stock A
that sell for $48 per share and 165 shares of Stock B that sell for $29 per share?
Total dollar value of the portfolio = 135 × $48 + 165 × $29 = $11, 265.
Weight for Stock A = 135 × $48/$11, 265 = 57.52%.
Weight for Stock B = 1 − 57.52% = 42.48%
- You own a portfolio that has $2,650 invested in Stock A and $4,450
invested in Stock B. If the expected returns on these stocks are 8% and 11%,
respectively, what is the expected return on the portfolio?
( qs 2 homework)
Weight for Stock A = $2, 650/($2, 650 + $4, 450) = 37.32%.
Weight for Stock B = 1 − 37.32% = 62.68%.
Expected return on the portfolio is the weighted sum of the individual expected
returns, thus equal to 37.32% × 8% + 62.68% × 11% = 9.88%
You own a portfolio that is 35% invested in Stock X, 20% in Stock Y, and
45% in Stock Z. The expected returns on these stocks are 9%, 17%, and 13%,
respectively. What is the expected return on the portfolio?
12.40%.
qs 3
qs 6 homework
12.60%.
Qs 7 homework
Var(RA) = 0.002023
Var(RB ) =0.019363.
σ(RA) = 4.5%
σ(RB ) = 13.92%
Qs 9 homework
E[Rp] = 13.08%
Var(Rp) = 0.013767.
- You own a stock portfolio invested 20% in Stock Q, 30% in Stock R, 35%
in Stock S, and 15% in Stock T. The betas for these four stocks are .84, 1.17,
1.08, and 1.36, respectively. What is the portfolio beta?
βp = 20% × 0.84 + 30% × 1.17 + 35% × 1.08 + 15% × 1.36 = 1.101.
A stock has a beta of 1.15, the expected return on the market is 10.3%,
and the risk-free rate is 3.8%. What must be the expected return on this stock
be?
11.28%.
qs 13 homework
- A stock has an expected return of 10.2%, the risk-free rate is 4.1%, and
the market risk premium is 7.2%. What must the beta of this stock be?
β = 0.8472.
Qs 14 homework
A stock has an expected return of 11.05%, its beta is 1.13, and the
risk-free rate is 3.6%. What must the expected return on the market be?
E[RM ] = 10.19%
qs 15 homework
Stock Y has a beta of 1.2 and an expected return of 11.4%. Stock Z has a
beta of .80 and an expected return of 8.06%. If the risk-free rate is 2.5% and
the market risk premium is 7.2%, are these stocks correctly priced?
E[RY ] = 2.5% + 1.2 × 7.2% = 11.14% < 11.40% and
E[RZ ] = 2.5% + 0.80 × 7.2% = 8.26% > 8.06%
Stock Y delivers higher expected return than the
CAPM, hence it is under-priced. On the other hand, stock Z delivers lower
expected return than the CAPM, hence it is over-priced
qs 19 homework
Stock Y has a beta of 1.2 and an expected return of 11.4%. Stock Z has a
beta of .80 and an expected return of 8.06%. If the risk-free rate is 2.5% and
the market risk premium is 7.2%, are these stocks correctly priced?
What would the risk-free rate have to be for the
two stocks to be correctly priced?
Rf = 1.38%
qs 20 homework
Qs 23 homework
a.b.c
look at answer sheet
Qs 24 homework
wC = 0.380155
risk-free asset= $114, 845
Qs 26 homework
look at answer sheet
What is the risk-reward ratio
The risk-reward ratio is a mathematical calculation used by investors to measure the expected gains of a given investment against the risk of loss.
According to the capital asset pricing model:
There is an inverse relationship between risk and return.
A stock which earns a higher rate of return than the market should have a beta which is greater than 1.0.
An increase in the risk-free rate without a corresponding increase in the market rate of return indicates that the risk premium for a stock with a beta of.8 will increase.
A stock with a beta of 1 will see its expected rate of return increase by 20% if its beta rises to 1.2, all else constant.
A stock with a beta of 2.0 will see its return decline by 2% should the risk-free rate decline from 3% to 2%, all else constant.
B
You would like to combine a risky stock with a beta of 1.8 with Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market. What percentage of the portfolio should be invested in Treasury bills?
Multiple Choice
40%
44%
52%
56%
60%
44%
What is the expected market return if the expected return on asset A is 16% and the risk-free rate is 7%? Asset A has a beta of 1.2.
Multiple Choice
9.5%
14.5%
16.5%
17.5%
20.5%
14.5%
The Inferior Goods Co. stock is expected to earn 14% in a recession, 6% in a normal economy, and lose 4% in a booming economy. The probability of a boom is 20% while the probability of a normal economy is 55% and the chance of a recession is 25%. What is the expected rate of return on this stock?
Multiple Choice
6.00%
6.72%
6.80%
7.60%
11.33%
6.00%
The standard deviation of a portfolio will tend to increase when:
Multiple Choice
A risky asset in the portfolio is replaced with Treasury bills.
One of two stocks related to the airline industry is replaced with a third stock that is unrelated to the airline industry.
The portfolio concentration in a single cyclical industry increases.
The weights of the various diverse securities become more evenly distributed.
What is the variance of a portfolio consisting of $2,000 in stock B and $8,000 in stock C?*look at table problem 6 quiz
0.00000
0.00084
0.000000
You want your portfolio beta to be 1.30. Currently, your portfolio consists of $16,000 invested in stock A with a beta of 1.20 and $11,000 in stock B with a beta of 1.10. You have another $25,000 to invest and want to divide it between stock C with a beta of 1.70 and a risk-free asset. How much should you invest in the risk-free asset?
Multiple Choice
$3,647
$3,786
$3,836
$3,897
$3,984
$3, 647
What is the value of systematic risk for a portfolio with 75% of the funds invested in A and 25% of the funds invested in B?
Multiple Choice
0.98
1.13
1.28
1.40
1.60
- look at table qs 8 quiz
1.13
- look at table qs 9 quiz
Which one of the following stocks is correctly priced if the risk-free rate of return is 3.2% and the market risk premium is 8.4%?
a
b
c
d
c
What is the standard deviation of the returns on a stock given the following information?
* look at table qs 10 quiz
7.24%
7.64%
7.24%
