BFC5935 Portfolio Management Theory
Final Workshop
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Q1 – Asset & Investment
1. Using a diagram, discuss the three components of an investor’s required rate of return on an
investment.
risk free rate
risk premium
inflation
2. Discuss how an individual’s investment objectives and asset allocation may change as he or she
goes through accumulation, consolidation and distribution phases of life cycle. Explain your reasons.
Accumulation phase : Early to middle years of working career; the age between 20 years old to 35 years old. So they are net worth may is usually small and debt
maybe heavy.
Consolidation phase: past midpoint of careers. The age between 40 years old to 55 years old. The people of this age which earnings now is more than living
expenses, so they have balance can be invested; moderately high- risk investments maybe attract them.
Spending/Gifting phase: Begins after retirement; the age after 55 years old. The people of this age usually cannot take risks, however they still want investment
values to keep peace with inflation.
3. During the past five years, you owned two stocks that had the following annual rate of return:
(a) Compute the arithmetic means of annual rates of return for each stock and the market index.
Which stock is most desirable by this measure? Why?
(b) Compute the standard deviations of the annual rate of return for each stock and the market index.
By this measure, which is the preferred stock? Why?
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(c) Compute the coefficients of variation for each stock and the market index. By this relative
measure of risk, which stock is preferred? Explain.
(d) Compute the geometric mean of the rate of return for each stock and the market index.
Discuss the difference between arithmetic mean returns and the geometric mean returns for each
stock and the market index.
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4. The following are monthly percentage price changes for two market indexes.
Compute the following.
1. Expected monthly rate of return for each market index.
2. Standard deviation for each index.
3. The correlation coefficient between the two indices.
4. Using the answers from above parts (as applicable), calculate the expected return and
standard deviation of a portfolio consisting of equal parts of DJIA and the S&P500.
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5. Based on the following share price and shares outstanding information, answer the questions
below:
a Share
split two for one during the year.
(i) Calculate the percentage change in the value of a price‐weighted index.
Calculate the percentage change in the value of a market‐value weighted index.
(ii) Explain the difference in results between the two indexes.
(iii) Calculate the results for an unweighted index and discuss why these results differ from the other
two indexes.
Q2 – Portfolio theory
6. Using a diagram analyse the components of the portfolio management process.
1. Policy statement
2. examine current and project financial, economic, political, and
social conditions
3. Implement the plan by constructing the portfolio
4. Feedback loop
7. A portfolio contains the following two assets
1). Refer to the information above and calculate the expected return of the portfolio.
2). Refer to the information above and calculate the standard deviation of the portfolio.
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8. You are evaluating various investment opportunities currently available and you have calculated
expected returns and standard deviations for five different well-diversified portfolios of risky assets:
a. For each portfolio, calculate the risk premium per unit of risk that you expect to receive [E(R)
-RFR]/SD). Assume that the risk-free rate is 3.0 percent.
b. Using your computation in Part a, explain which of these five portfolios is most likely to be the
market portfolio. Use your calculations to draw the capital market line (CML).
c. If you are only willing to make an investment with SD = 7.0%, is it possible for you to earn a
return of 7.0 percent?
d. What is the minimum level of risk that would be necessary for an investment to earn 7.0 percent?
What is the composition of the portfolio along the CML that will generate that expected return?
e. Suppose you are now willing to make an investment with SD = 18.2%. What would be the
investment proportions in the riskless asset and the market portfolio for this portfolio? What is the
expected return for this portfolio?
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9.
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Q3 – Market Efficiency
10. Briefly discuss the problems related to fundamental analysis that are considered as advantages of
technical analysis.
11. Briefly discuss the implications of the efficient market hypothesis for investment policy as it
applies to:
(i) Technical analysis, and
(ii) Fundamental analysis.
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12. Efficient Market Hypothesis EMH
A market is efficient if security prices immediately and fully reflect all available relevant information.
We divided into three sub-hypotheses depending on the information set involved.
➢ Weak-form EMH
Current prices reflect all security-market historical information, including the historical sequence of
prices, rates of return, trading volume data, and other market-generated information.
This implies that past rates of return and other market data should have no relationship with future
rates of return.
In short, prices reflect all historical information.
➢ Semi-strong-form EMH
Current security prices reflect all public information, including market and non-market information.
This implies that decisions made on new information after it is public should not lead to above
average risk-adjusted profits from those transactions.
In short, prices reflect all public information.
➢ Strong-form EMH
Stock prices fully reflect all information from public and private sources.
This implies that no group of investors should be able to consistently derive above-average risk
adjusted rates of return.
This assumes perfect markets in which all information is cost-free and available to everyone at the
same time.
In short, prices reflect all public and private information.
Behaviour Finance
Prospect Theory 人们更加在乎输赢，而不是总财富 并且是厌恶损失的
Disposition Effect
▪
Investors holding an asset that is currently making a loss will be reluctant to sell the asset
▪
This is because the convex value function over losses predicts that an investor will prefer a
gamble to a realised loss（想赌一把 看看资产价格会不会上升，就是因为人们不喜欢损
失，才开始有赌一把的心理）
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▪
Investors will behave as if they were loss averse
Fear/Pain of Regret 越不放手 恨得越深
Another mental error that can affect decision making is an excessive focus on the potential feelings
of regret at having made a poor decision. This type of error is rooted in most individuals' dislike for
admitting they are wrong. 由于自己不愿意承认自己错了 所以做错了一个决定会更加后悔
The fear of regret also leads to the disposition effect.（不愿意放手）
Overconfidence 过度自信
Overconfidence causes people to misinterpret the accuracy of the information and overestimate the
skill in analysing it. 使得信息失真 高估自己的分析能力
Risk Perceptions
People’s perception of risk appears to vary.
An important factor is past outcome.
People generally are willing to take more risk after earning gains and less risk after losses.（根据过去
的表现做决策）
Cognitive Dissonance 意识扭曲
People tend to ignore, reject or minimize any information that conflicts with their positive self image.
Evidence that cannot be denied is accommodated by a change in beliefs.
人们是不愿意去相信或者接受与自己想法不一样的事情 但是想法会一直发生变动
Mental Accounting 精神账户 对每件事情有自己的看法
Having ‘home’ and ‘Car’ in separate mental accounts
Combining them together would have maximize their wealth 需要考虑全部因素 而不是单一因素
Portfolios are consistent with the investor’s goals (reflecting risk)
Investors focus on asset variance. This result inefficient portfolios. 只关注风险是无法做出正确决
定的
Representativeness 代表性 认为名牌大学就什么专业都好
‘Are the stocks of good companies good investments?’
Classifications are made based on a limited number of shared qualities.
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The effect of representativeness in investment decisions can be seen when certain shared qualities are
used to classify stocks.
Anchoring 锚定效应，指用户对事物的认知总会根据第一印象或信息形成一个自己对此事物的
片面认知
Some decision making errors result from mental shortcuts that are a normal part of the way we think.
Anchoring is the psychologists' term for one shortcut the brain uses. 对事物之前的认知减少了大脑
的思考
Q4 – Asset Pricing Models
13. Arbitrage Pricing Theory & Capital Asset Pricing Model
1). Consider a two-factor APT model where the first factor consists of changes in the 30-year T-bond
rate and the second factor is the percent growth in GNP. Based on historical estimates you determine
that the risk premium for the interest rate factor is 0.02, and the risk premium on the GNP factor is
0.03. For a particular asset, the response coefficient for the interest rate factor is 1.2, and the response
coefficient for the GNP factor is 0.80. The rate of return on the zero-beta asset is 0.03. Calculate the
expected return for the asset.
2). A security with beta of 0.8 has an expected rate of return of 14%. If the risk-free rate is 5%, and
you expect the rate of return on the market portfolio to be 15%, should you invest in this security?
What is the fund’s alpha?
14. Assume that asset A has an expected return of 8.5% with a beta of 0.9 and asset B has an
expected return of 10.5% with a beta of 1.4. If the two assets are correctly priced on the security
market line, what is the return of the market portfolio? What is the risk-free rate of return?
15. An analyst expects a risk-free return of 4.5 percent, a market return of 14.5 percent, and the
returns for Stocks A and B that are shown in the following table.
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Show on a graph
(i) where Stocks A and B would plot on the security market line (SML) if they were fairly valued
using the capital asset pricing model (CAPM);
(ii) where Stocks A and B actually plot on the same graph according to the actual returns in the table.
Q5 – Bond analysis
16. A coupon bond is currently sold at $1,280. The face value of the bond is $1,000 and the annual
coupon rate is 10%. The bond will expire in three years and coupon payments are made semi
-annually. Suppose the interest rate is 8%, is the bond currently overvalued or undervalued?
17. A 2-year maturity bond with a face value of $1,000 makes annual coupon payments of $80 and
selling at $1,080.
i) What is the current yield of the bond?
ii) What is the yield to maturity (YTM) of the bond?
iii) What is the price of the bond if inflation is expected to increase interest rate by 2 percent?
18. Consider the following bonds: Which of the bonds A to D is most sensitive to changes in interest
rates? Explain your answer without using calculations.
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19. You plan to buy a five‐year bond (face value $1,000) with 8% annual coupon payments. The
bond has yield to maturity of 8%.
(i) Calculate the Macaulay duration of the bond.
(ii) What is the modified duration of this bond?
20. Indicate briefly what you understand by active portfolio management and passive portfolio
management.
21. What is Immunization for bond portfolio management? Which two risk will be cancelled out in
this process?
22. Briefly explain the different forms of term structure of interest rates and three theory behind
them.
23. The 4-year spot rate is 9.45%, and the 3-year spot rate is 9.85%. What is the 1- year forward rate
three years from today?
A. 8.258%.
B. 9.850%.
C. 11.059%.
24. Given the following spot and forward rates:
Current 1-year spot rate is 5.5%.
One-year forward rate one year from today is 7.63%.
One-year forward rate two years from today is 12.18%.
One-year forward rate three years from today is 15.5%.
The value of a 4-year, 10% annual-pay, $1,000 par value bond is closest to:
A. $996.
B. $1,009.
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C. $1,086.
Q6 – Security Analysis I & II
25. P/E multiplier
The Sigma Pharmaceuticals Company sells at $32 per share, and Dr Robert Baker, the CEO of Baker
Financial Research firm, estimates the latest 12‐month earnings are $4 per share with a dividend
payout of 50 %. Dr Baker’s earnings estimates of Sigma are very accurate.
(i) Calculate Baker’s current P/E ratio for Sigma. If an investor expects earnings to grow by 10% a
year, estimate the projected price of Sigma for the next year if the P/E ratio remains unchanged.
(ii) Dr Baker analyses the data and estimates that the payout ratio of Sigma will remain the same.
Assume that the expected growth rate of dividends is 10%, and an investor has a required rate of
return of 16%. Recommend to a potential investor whether Sigma is a good buy. Justify your
recommendation.
26. Johnson Corporation currently pays $2.50 dividend per share on its ordinary shares. Due to its
impressive research and development facilities, the company’s earning is expected to grow rapidly
during the next three years. The company directors projected that the dividend growth rate will be 15
percent per year for the next three years and continue to grow at a rate of 6 percent thereafter.
▪
What is the value of the ordinary share of John Cabin Corporation if the required rate of
return is 16%?
▪
What is the value of the ordinary share if the growth has been reduced to zero for the first
three and 6 percent thereafter?
27. What is Asset allocation? Explain the differences between strategic asset allocation (SAA) and
tactical asset allocation (TAA).
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28. What is the Dow theory, Explain it.
29. What are the different stages of business cycle and the characteristic of each?
30. What is industry cycle, draw a diagram and explain it.
31. What is the difference between “Top-down” and “Bottom-up”?
Q7 – Portfolio Management I & II
32. What are the trade-offs involved when constructing a portfolio using a full replication versus a
sampling method?
33. What is a Momentum strategy and Contrarian strategy? What is the difference between Value
stock and Growth stock?
34. Below is a table of data on the average returns and risks of several portfolios for the last 10 years.
(i) Calculate Sharpe, Treynor and Jensen’s Alpha measures for the above risky asset portfolios. In
calculating Jensen’s Alpha assume that the above information is only for one year and not for ten
years.
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(ii) Prepare a table ranking all the risky asset portfolios using the above three measures.
Discuss the differences in rankings indicating probable causes.
35. Portfolio performance attribution analysis
Actual Return
Actual Weight
Benchmark Weight
Benchmark Return
Equity
2%
0.7
0.6
2.5%
Bonds
1%
0.2
0.3
1.2%
Cash
0.5%
0.1
0.1
0.5%
a. What was the manager’s return in the month? What was her outperformance or
underperformance?
b. What was the contribution of the selection effect for the manager?
c. What was the contribution of the allocation effect for the manager?
36. The table below documents the returns generated by a fund manager and a benchmark portfolio.
Bogey Portfolio
Component
Equity
Bonds
Cash
Managed Portfolio
Component
Equity
Bonds
Cash
Index
S&P500
Lehman Index
Money Market
Benchmark
Weight
0.6
0.3
0.1
Return on
Index
5.8100%
1.4500%
0.4800%
Return on Bogey
Portfolio
Return
3.4860%
0.4350%
0.0480%
3.9690%
Portfolio
Weight
0.7
0.07
0.23
Actual
Return
7.2800%
1.8900%
0.4800%
Portfolio
Return
5.0960%
0.1323%
0.1104%
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Return on Managed portfolio
5.3387%
Excess Return of managed
portfolio
1.3697%
Use this data to attribute return between security selection and asset allocation.
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