ADMS 4501 Lecture Notes - Growth Stock, Arbitrage Pricing Theory, Arbitrage

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pearimpala756

24 Jan 2013

School

York University

Department

Administrative Studies

Course

ADMS 4501

Professor

Lois King

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Document Summary

For an average portfolio, managers are looking at 8% return. Assumptions : efficient investors , risk free rate, homogenous expectation, ,fractional holding, ignore inflation and taxes, and fair pricing( market efficiencies) Risk free asset has zero standard deviation, variance, correlation and covariance ( with other assets) Note that the tangent cml to the markowitz frontier is the best possible choice giving you a balanced risk return. Total risk = systematic risk + unsystematic risk ( which can be eliminated via diversification) Beta is the measure of risk in this case. Where sml shows a balance between the risk and return for a particular asset. Underpriced assets would be purchased by arbitrageur and therefore move the price higher so as to bring them to the sml and bring about efficiency and vice versa. Beta is not stable and has various methods for calculation. Note that bank stocks are typically less volatile as compared to technology stocks.

Related Questions

1. If we are able to eliminate all of the unsystematic or diversifiable risk in a portfolio then, what is the result?

a.

a risk-free portfolio
b.
a portfolio that has an expected return of zero
c.

a portfolio that contains only systematic risk

2. A portfolio consists 20% of a risk-free asset and 80% of a stock. The risk-free return is 4%. The stock has an expected return of 15% and a standard deviation of 30%. Whatâs the expected return of the portfolio?

a.
9.5%
b.
15.0%
c.
12.8%

d.
2%

3. The risk-free rate is 5% and the expected return on the market portfolio is 13%. A stock has a beta of 1.5, what is its expected return?

a.
12%
b.
19.5%
c.

17%

4. For what value of the correlation coefficient for the returns of a pair of stocks will the benefits of diversification the largest?

a.

1.0
b.

-1.0
c.

0.0
d.

0.5

5. Which of the following is an example of systematic risk?
a.
IBM posts lower than expected earnings.
b.
The overall stock market becomes more risky due to super fasting trading algorithms.
c.

Intel announces record earnings.

6. According to the CAPM (capital asset pricing model), the security market line is a straight line. The intercept of this line should be equal to

a.
zero
b.
the expected risk premium on the market portfolio
c.
the expected return on the market portfolio
d.
the risk-free rate

7. A portfolio has 40% invested in Asset 1, 50% invested in Asset 2 and 10% invested in Asset 3. Asset 1 has a beta of 1.2, Asset 2 has a beta of 0.8 and Asset 3 has a beta of 1.8, whatâs the beta of the portfolio?

a.
0.80
b.
1.06
c.
1.27

8. Suppose you can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios has the best return relative to risk. (Hint: Calculate Sharpe Ratios the ratio of risk premium to standard deviation for each portfolio)

a.
portfolio with a standard deviation of 15% and an expected return of 12%
b.
portfolio with a standard deviation of 12% and an expected return of 9%
c.
portfolio with a standard deviation of 25% and an expected return of 18%
d.
portfolio with a standard deviation of 19% and an expected return of 15%

9. Which statements are TRUE regarding risk and return?

Statement I:
Diversification is the process of removing systematic risk from a portfolio.
Statement II:
In general, the greater the risk, the greater the return required by an investor.
Statement III:
Investors should focus on real returns if they are concerned about the purchasing power of their wealth.

a.
Statements II and III only
b.
Statement I only
c.
Statements I and III only
d.
Statements I and II only

10. The beta of the risk-free asset is:
a.

1.0
b.

0.5
c.

0.0
d.

-1.0

Hi guys could someone help me and explain in detail the two fundamental principles of investments â the risk/return tradeoff and diversification. Also, describe how asset allocation and the correlation of various securities within asset classes impact the riskiness of an investorâs portfolio.

I found an answer but it seems to me very long and not sure about it so can you help me out guys

ANS:

Risk /Return Tradeoff

Risk, return and liquidity are three dimensions of investment decision. Risk/Return trade off considers two dimension ie risk and return. As risk of an investment increases , its expected return will decrease. Risk is measured by volatility of return which can be statistically obtained by standard deviation of return. Higher the standard deviation, higher will be volatility of return and higher the risk

Risk can be also measured as a relative risk compared to the market. This is measured by stock beta with reference to a market index. Higher the beta, higher the value of stock Beta, higher will be the risk .

Investors seeking higher return will need to take higher risks.

Treasury bonds are almost risk free assets. This has the lowest rate of return. Stocks have higher risk , hence have higher expected return. High beta stocks will have higher risk and higher returns.

An investor should understand his risk taking ability and will have to make a trade off between risk and return depending on his risk apetite.

Diversification:

There is a saying, do not put all your eggs in one basket. The reason is that it has higher risk if all eggs are in one basket. If the eggs are distributed in different basket, risk of loss decreases.

Same principle is applied in investment. Diversification reduces risk.

If one invests in different classes of assets like bonds, stock, commodities and properties âhis risk is likely to reduce. Reduction in return in one asset is likely to be compensated by return in other asset.

Within one class of asset also, there should be diversification to reduce risk.

For example one stock âA âmay have expected return of 10% and standard deviation of 5%.This risk can be reduced by diversification in number of assets and the ratio of Risk/return can be decreased.

If we diversify and instead of investing 100% in stock A, we invest 60% in âAâ and 40% in another stock âBâ having expected return15% and standard deviation of 8%.assume the correlation between the two assets are 0.5

Portfolio return=wa*Ra+wb*Rb

Wa=Weight of asset A=0.6

Wb=Weight of asset B=0.4

Ra=Return of A=10%

Rb=Return of B=15%

Sa=Standard deviation of A=5%

Sb=Standard deviation of B=8%

Corr(a,b)=Correlation of A & B=0.2

Portfolio return=0.6*10+0.4*15=12%

Portfolio Variance=(wa^2)*(Sa^2)+(wb^2)*(Sb^2)+2wa*wb*Cov(a,b)

Cov(a,b)=Corr(a,b)*Sa*Sb=0.1*5*8=4

Portfolio Variance=(0.6^2)*(5^2)+(0.4^2)*(8^2)+2*0.6*0.8*4=23.08

Portfolio standard deviation=Square root of Variance=(23.08^0.5)=4.8%

The diversification has increased return and reduced risk

Stock A was giving 10% return with 5% standard deviation. With diversification of portfolio we have 12% return and 4.8% standard deviation. Risk return ratio is decreased.

It may be noted that, higher the correlation between assets in the portfolio, higher will be risk in terms of standard deviation. Hence it is better to diversify with uncorrelated assets.

Diversification reduces unsystematic risk,but it cannot reduce systematic risk of overall market or economy

CONCEPTS IN THIS CASE

expected return
risk
portfolio choice
diversification
systematic risk
nonsystematic risk
beta
capital asset pricing model
arbitrage pricing

Your supervisor has asked that you quantify the effects of diversification using three potential portfolios. The information given regarding each portfolio is as follows:

Probability	Return (%) on Security A	Return (%) on Security B	Return (%) on Security C
.20	8	24	16
.30	10	16	10
.30	12	12	12
.20	14	17	6

Using the information above, calculate the following for each individual security:

What is the expected return for security A?

What is the expected return for security B?

What is the expected return for security C?

What is the variance of the return for security A?

What is the variance of the return for security B?

What is the variance of the return for security C?

Using the information above, calculate the following for each pair of securities:

What is the covariance of securities A and B?

What is the covariance of securities A and C?

What is the covariance of securities B and C?

If your firm makes equal investments in securities A and B (50% in each):

What is the expected return of the portfolio that combines A and B?

What is the variance of the portfolio that combines A and B?

If your firm makes equal investments in securities A and C (50% in each):

What is the expected return of the portfolio that combines A and C?

What is the variance of the portfolio that combines A and C?

If your firm makes equal investment in securities B and C (50% in each):

What is the expected return of the portfolio that combines B and C?

What is the expected variance of the portfolio that combines B and C?

Given the results of your work in questions 3, 4, and 5 above, which portfolio would you recommend to your supervisor? Explain.

You have searched online resources and found the beta of each security. Security A has a beta of 1.0, security B has a beta of .50 and security C has a beta of 1.50. If the risk-free interest rate is 5% and the expected return for the market portfolio is 12%:

What is the CAPM risk premium for security A?

What is the CAPM risk premium for security B?

What is the CAPM risk premium for security C?

How would your definition of the risk premium change if you used the Arbitrage Pricing Theory (APT) equation?

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ADMS 4501 Lecture Notes - Growth Stock, Arbitrage Pricing Theory, Arbitrage

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