Question 1 The picture below represents the methodology to forecast equity returns used by Invesco. As you can see their expected return is the sum of three components: Total Yield (a slightly modified version of the dividend yield), Earnings Growth and Valuation Change. Explain in layman terms, without using any formula, what is the Valuation Change component. Try to capture the economic intuition behind this concept. Under which economic circumstances this quantity could be negative? Question 2 The excel file Question_2.xlsx contains the time series of the Cyclically Adjusted Price Ratio for the US from 1900 to 2020. Estimate the Valuation Change component in May 2020. In this calculation you need an estimate of the ͞Long Term Aǀerage ValƵe͟ of CAPE͘ YoƵ coƵld Ƶse a ǀery long (from 1900) or a not-so-long (last 20-30 years) period to calculate this average. Would your result differ? Can you provide an economic intuition of why? Teaching materials and exam resources provided to you at UTS are protected by copyright. Students are reminded that copying or sharing of these materials can constitute misconduct. Page 4 of 8 Question 3 The following Table has the portfolios your bank is offering to your customers. The data is also available, for your convenience, in the file Question_3.xlsx. Portfolio N. % of Equity % of Bonds Exp Return St. Deviation 1 5% 95% 2.35% 2.44% 2 20% 80% 3.40% 4.42% 3 35% 65% 4.45% 6.70% 4 50% 50% 5.50% 9.04% 5 65% 35% 6.55% 11.42% 6 80% 20% 7.60% 13.80% 7 95% 5% 8.65% 16.20% You have just interviewed a new client who: x Cannot tolerate, psychologically, short-term losses more severe than -10%. x Would like to bring her net worth from $1M to $1.5M over the next 10 years. Which portfolio would you offer to the client? You do not have to report your calculations, but you need to explain where your numbers come from. Also try to explain to your client how well this portfolio satisfies her requirements. Teaching materials and exam resources provided to you at UTS are protected by copyright. Students are reminded that copying or sharing of these materials can constitute misconduct. Page 5 of 8 Question 4 Your boss has been using resampling to build an efficient frontier for one of your institutional clients. Below are the outputs from two of these simulations. Your boss is a bit confused because both frontiers have been built using the same assets and the same expectations. The only difference is the parameter T, the length of the simulated sample, that is 5 in one case and 40 in the other case (given that the client is an institution with a very long investment horizon). Can you help your boss remember which frontier comes from the simulation with T=5 and which one comes from the simulation with T=40? Can you explain to your boss, in layman terms, why the change in this parameter leads to these different results? Resampled Frontier N. 1 1 2 3 4 5 6 7 8 9 10 Portfolio Number 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Asset 1 Asset 2 Asset 3 Asset 4 Asset 5 Asset 6 Asset 7 Asset 8 Asset 9 Resampled Frontier N. 2 1 2 3 4 5 6 7 8 9 10 Portfolio Number 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Asset 1 Asset 2 Asset 3 Asset 4 Asset 5 Asset 6 Asset 7 Asset 8 Asset 9 Composition % Composition % Teaching materials and exam resources provided to you at UTS are protected by copyright. Students are reminded that copying or sharing of these materials can constitute misconduct. Page 6 of 8 Question 5 You have been tasked to study the determinants of equity returns in a new market where your firm is looking to invest. You take all the stocks in the market and run the following regression: �௜,ଶ଴ଵସିଶ଴ଵଽ ൌ � ൅ �ଵ�௜,ଶ଴ଵଷ ൅ �ଶ�௜,ଶ଴ଵଷ ൅ �ଷ��௜,ଶ଴ଵଷ ൅ � Where: x �௜,ଶ଴ଵସିଶ଴ଵଽ is the return of stock � between 2014 and 2019 x �௜,ଶ଴ଵଷ is the beta of stock � measured at the end of 2013 x �௜,ଶ଴ଵଷ is the market capitalization of stock � measured at the end of 2013 x ��௜,ଶ଴ଵଷ is the P/E ratio of stock � measured at the end of 2013 After running this regression, you obtain the following coefficients and T-statistics Coefficient Value T-Stat � 0.15 0.45 �ଵ -0.75 -1.12 �ଶ -0.45 -2.5 �ଷ -0.78 -3.2 From these numbers what do we learn about: x The CAPM in this country x The size premium in this country x The value premium in this country x Momentum in this country Question 6 In the Factsheet for their Large Cap Multi-Style Fund (analyzed in class and available in UTS Online), AQR explains, in the methodology section that, “Combining exposures to all three styles in an integrated portfolio can help reduce portfolio turnover and minimize transaction costs”. Can you explain, intuitively, why this happens? Teaching materials and exam resources provided to you at UTS are protected by copyright. Students are reminded that copying or sharing of these materials can constitute misconduct. Page 7 of 8 Question 7 Your boss is assessing the relative quality of two portfolio strategies. The results of an extensive backtesting are reported in the following table Market Strategy 1 Strategy 2 Mean Return 7.0% 9.4% 9.4% St. Deviation 16.0% 14.7% 10.7% Active Return 2.4% 2.4% Tracking Error 3.7% 7.7% Both strategies haǀe the same backtesting retƵrn͕ so LJoƵr boss is determined to choose the ͞less riskLJ one͘͟ After looking at the numbers he is quite confused. Can you help him to understand the numbers in the table and determine which portfolio is safer? Question 8 In the file Question_8.pdf you will find an article published in the Financial Times in 2015. In this article William Sharpe͕ the Nobel LaƵreate ǁho ͞inǀented͟ the CAPM͕ saLJs that smart-beta strategies (specifically the second-wave strategies referenced in the article) “By definition […] must contain the seeds of their own destruction”. Can you explain this concept in simple terms for a client with only moderate understanding of finance? Question 9 Making reference to the same article and problem analysed in Question 8, as a portfolio manager how would you build a successful smart-beta portfolio avoiding the risk described by William Sharpe? [Question 10 in the next page!] Question 10 Below is a snippet of Matlab code. for i = 1:100 result_1 = mvnrnd(input_1, input_2, 12); result_2 = mean(result_1, 2); result_3(i,1) = min(result_2); end Knowing that: x Input_1 is a 1x5 matrix x Input_2 is a 5x5 matrix a) Explain what each of the 5 lines of code does and describe the size of all the result_ variables. b) Assuming that the numbers in Input_1 are the expected monthly returns of 5 asset classes, and that Input_2 is the monthly var-cov matrix, what is the economic interpretation of the numbers in result_3? Teaching materials and exam resources provided to you at UTS are protected by copyright. Students are reminded that copying or sharing of these materials can constitute misconduct.