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What is the effect on the cost of equity (and the weighted average cost of capital) underan imputation tax system, compared to a classical tax system (assuming shareholdersare able to utilise franking credits)...

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EBS - Chair of Corporate Finance & Higher Education Finance BSC Portfolio Management

ST 2021

EVALUATED EXERCISE - SOLUTIONS (MIDTERM EXAM) QUESTION 1 (2 points) David Bowie bonds were basically securitized song royalties where investors would earn their share in his future proceeds for the next ~10 years. This was the first security which was backed by intellectual property as the underlying asset. Investors believed that purchasing the bonds will provide them with a safe and steady long-term investment. Investors’ rationale was that it was highly unlikely that such a famous artist will lose his popularity and thus album sales. Little did they know that the entire music industry would be changing soon thereafter. Furthermore, yield was rather high and provided a better investment opportunity than average corporate bonds. A substantial number of investors also just allocated their funds to the bond as they were huge fans of Bowie and his music. Finally, we should not forget that a new type of risk was introduced to the financial market giving investors add portfolio diversification opportunities. One of the arguments above gives you full credit.

QUESTION 2 (8 points) – this question was identical to Q2 of the morning exam First, you have to identify the respective portfolio weights where w stands for asset 1: 0.18 = 𝑤 𝑥 0.15 + (1 − 𝑤) 𝑥 0.20 𝑤 = 0.40 1 − 𝑤 = 0.60 In order to realize 18% portfolio return, Dorothee has to invest 40% in fund (1) and 60% in fund (2). 𝜎 = √0.42 𝑥 0.1225 + 0.62 𝑥 0.36 + 2 𝑥 0.4 𝑥 0.6 𝑥 0.084 𝜎 = 0.4353 The net volatility increase is also 0.4353 as she was invested in a risk-free asset before where volatility is 0.

EBS - Chair of Corporate Finance & Higher Education Finance BSC Portfolio Management

ST 2021

QUESTION 3 (8 points) a.

Financial innovation makes markets more complete, thereby enabling investors to better optimize their future consumption plans. Any type of allocation can be realized if there as many future states of the world as there are assets (= market completeness). We must however assume that markets are generally incomplete – the future is just too complex to be captured by the assets available for investors. See Session 4, Slide 20.

b.

Financial innovation improves the risk-return ratio in the context of extended diversification. Through financial innovation, e.g., securitization of multiple assets into one single asset, investors can potentially improve exp. returns while lowering the volatility they are exposed to. Through making new risks tradeable, investors can also optimize their portfolio’s risk-return ratio, e.g., by hedging out risks through simple option strategies. Nevertheless, you can also argue that this might be potentially also go in the wrong direction, e.g., in the financial crisis where financial innovations created a lot of additional risk. This was a theme for the course so far and has been particularly emphasized in sessions 3 and 4.

c. You needed to check whether the market is incomplete. Your first thought probably was: # states = # independent assets (market is complete and no point to have further financial innovation in the sense of creating more assets. But: A closer look shows 𝐴3 = 𝐴1 − 𝐴2 . Hence, # states > # independent assets and therefore financial innovation is beneficial. We worked through a similar number example in class. d. We have discussed this in the context of Session 3. It is equivalent to Session 4, Slide 4. Portfolio w/ financial innovation

Portfolio w/o financial innovation

EBS - Chair of Corporate Finance & Higher Education Finance BSC Portfolio Management

ST 2021

QUESTION 4 (8 points) a. This statement is False. Please consult Slide 7 of Session 3-2. Any point on this line can potentially be an optimum for risk-averse investors with convex indifference curves. A picture-perfect answer would have used this graph with exemplary indifference curves and a short explanation. b. Given perfect negative correlation, combining asset 2 and asset 3 can create a portfolio with zero risk. 𝜔3 = 𝑠𝑦𝑛𝑡ℎ𝑒𝑡𝑖𝑐

𝑟𝑓

6% 8% + 6%

= 0.43

= 0.43 ∙ 12% + 0.57 ∙ 8% = 9.72%

Hence, 𝑠𝑦𝑛𝑡ℎ𝑒𝑡𝑖𝑐

𝑟𝑓

𝑜𝑢𝑡𝑟𝑖𝑔ℎ𝑡

= 9.72% > 2% = 𝑟𝑓

An arbitrage opportunity exists where you can borrow at the outright rate and earn the synthetic rate. The arbitrage profit equals 7.72%. As discussed in the review session.

QUESTION 5 (4 points) i.

You assumed that the investor only chooses one asset. You determine the Sharpe ratios for assets 1 and 2: 𝑆ℎ𝑎𝑟𝑝𝑒 𝑅𝑎𝑡𝑖𝑜1 = 𝑆ℎ𝑎𝑟𝑝𝑒 𝑅𝑎𝑡𝑖𝑜2 =

0.12 − 0.04 =1 0.08 0.10 − 0.04 0.05

= 1.2

A rational investor would aim for maximizing her Sharpe Ratio. Thus, the investor would invest in asset 2 with the higher Sharpe Ratio. Asset 3 can be considered as the risk-free asset as it is not associated with any volatility. ii.

You assumed that the investor can invest in any mix of assets. Then the logic developed in Session 3.1, Slides 11-12 applies (actually, we are using the same numbers here as in class). You pick a combination of assets 1 and 3 which maximizes the Sharpe ratio (see above)....