Assumptions and conclusions of Arbitrage Pricing Model (APT)

1. What are the main assumptions and conclusions of Arbitrage Pricing Model (APT)? How might you estimate the APT factor premium associated with each factor? Compare and describe two methods carefully. Why might the more sophisticated method work better?
2. What are the differences among leading, coincident, lagging economic indicators? Pick one example (not composite indicator) for each of leading, coincident, lagging (three examples in total) and discuss why it is leading, coincident, or lagging.
3. What are the similarities and differences among global minimum variance (GMV), risk parity (RP), and low beta portfolios? Why might these portfolios outperform (as measured by Sharpe ratio) when they clearly do not have the maximal Sharpe Ratio in theory? Why might be some of the reasons for an investment consultant to not recommend these portfolios constructed from US equities given their seemingly superb performance characteristics when compared to the S&P 500?
4. An endowment fund uses a core-satellite approach to allocate amongst different managers. The managers’ active risk, active return, and allocations (in endowment portfolio) are given in following table. What is (are) the investor’s core position? Calculate the endowment fund’s overall active return, active risk, and information ratio. If you do not have enough information to make the calculation, list the assumptions you need and the reasons. Expected Active Return Expected Active Risk Allocation
   Passive Index 0.00% 0.00% 20%
   Enhanced Indexing 0.70% 1.50% 30%
   Active Manager A 1.00% 2.50% 25%
   Active Manager B 2.00% 3.00% 15%
   Active Manager C 2.40% 4.20% 10%
5. A define-benefit pension fund has following holdings in their fixed-income portfolio:

Bond Credit Rating Maturity (yr) Coupon Rate (%) Modified Duration Convexity Market Value of Position
A US Treasury 3.1 0.3 2.738 9.8 $50,000
B A1 9.8 7.5 6.452 56.2 $50,000
C Aa2 5.2 11.5 3.733 18.5 $50,000
D Agency 6.7 9.8 4.874 32.3 $50,000
E Aa3 12.1 1.8 10.921 128.4 $50,000
Total $250,000

i) Calculate modified duration for this portfolio. ii) the modified duration of pension’s liabilities is 6.50 years. Comment on immunization against interest rate risk; iii) how can you increase the convexity of the portfolio while keeping modified duration unchanged? iv) You forecast that both Treasury yields and credit spreads will decrease in the near future. How will you adjust the existing portfolio according to this view?

6. Please explain carefully different definitions of quality anomaly. Please explain data-snooping. How might you prove that quality is a true anomaly instead of a datamined result?
7. You are given stock returns for 350 stocks which have 40 years of monthly stock returns. You form a cap-weighted portfolio from these 350 stocks and back-test this portfolio against the S&P 500. You discover that this portfolio outperforms the S&P 500 by 9% per annum! How do you explain that? (Hint: you may have legit reasons whether this awesome outperformance is real or you may have made mistakes in backtest, which means that this awesome backtest result cannot be replicated in the real world.)
8. You have a portfolio with three assets. The forecasted inputs are showed in following table. Calculate expected marginal contribution to total risk (MCTR) and absolute contribution to total risk (ACTR) of each asset. Mean Portfolio Weight Covariance Matrix
   Asset 1 Asset 2 Asset 3
   Asset 1 8% 25% 0.00860 0.00823 0.00071
   Asset 2 10% 40% 0.00823 0.00972 -0.00313
   Asset 3 6% 35% 0.00071 -0.00313 0.03987
9. You have performance data for two portfolio managers and a common benchmark portfolio: Benchmark Manager A Manager B
   Weight Return Weight Return Weight Return
   Stock 0.6 -5.0% 0.5 -4.0% 0.3 -5.0%
   Bonds 0.3 -3.5% 0.2 -2.5% 0.4 -3.5%
   Cash 0.1 0.3% 0.3 0.3% 0.3 0.3%

i) Calculate the overall returns of benchmark, Manager A and Manager B. Did these managers under- or outperform the benchmark?
ii) Calculate asset allocation effect and security selection effect for both Manager A and B. Comment on what this performance attribution analysis tells you about managers’ performance?

10. What are the basic assumptions in efficient market hypothesis (EMH) and behavioral finance? List and briefly explain three forms of EMH. List one anomaly for each form of EMH that may violate that form of EMH (three anomaly examples in total). List one argument from EMH supporter and one argument from behavioral finance supporter regarding each anomaly example. 11.Following up Question 3 above, under what condition will GMV and risk parity be tangency portfolio? You must show mathematical proof to earn credit for this question.
11. Following up Question 8 above, you also have benchmark weight, which is 35% in Asset 1, 40% in Asset 2, 25% in Asset 3. Calculate marginal contribution to tracking error (MCTE) and absolute contribution to tracking error (ACTE). Specify which method do you use and the pros and cons of that method in the context of this question.