You work for a consulting firm. UE has just hired your team to make

recommendations on the composition of its endowment fund. UE is considering investing in a

broad selection of risky assets, ranging from bonds to cryptocurrencies. As a proxy for the different

asset categories, you decide to use appropriate ETFs and investment trusts. These include:

iShares Core FTSE 100 ETF (ISF.L)

iShares Core MSCI Total International Stock ETF (IXUS)

Vanguard Total Bond Market Index Fund ETF Shares (BND)

Vanguard S&P 500 ETF (VOO)

iShares U.S. Real Estate ETF (IYR)

Grayscale Bitcoin Trust (GBTC)

Due to the pandemic, UE has been relying more and more heavily on its endowment to

meet its budgets need in the past two years. After meeting with UEs Chief Financial Officer

(CFO), your manager identified several issues to be addressed and asked you to conduct the

analysis. In your analysis, assume the risk-free rate is 0% and ignore the effects of exchange rate

fluctuations. Also assume that UEs position is large enough that trading fees and transaction

costs are negligible. Do not include the risk-free asset in your recommendation because UEs

CFO is interested in the construction of its risky portfolio, not the complete portfolio. Use

historical monthly return from January 2016 to December 2020 to construct portfolios (note that

you need prices on 1/1/2021 to calculate returns for December 2020). Use data from January

2021 to August 2022 to evaluate portfolio performance unless otherwise instructed (e.g. Q1).

1. From January 2016 to December 2020, UEs risky portfolio invested 50% in the U.K.s

domestic equity market (proxied by ISF.L), 30% in the global equity market (proxied by

IXUS), and 20% in the bond market (proxied by BND). Refer to this portfolio as P0 and

assume that UEs asset allocation remained the same over this period. How well did P0

perform? Collect monthly historical data, calculate performance summary statistics, and

compare these statistics with those of the S&P500 index (proxied by VOO) over the same

period.

2. Do you recommend UE to expand its investment universe to include the U.S. equity (proxied

by VOO), real estate (proxied by IYR), and cryptocurrencies (proxied by GBTC)? Plot the

efficient frontier using the three asset categories that UE already invested in. Compare it

with the efficient frontier generated using all six asset categories UE is considering. Assume

there are no trading restrictions.

3. Assume there are no trading restrictions, and UE uses the historical averages to proxy for

expected returns. How should UE form its risky portfolio? Refer to this portfolio as P1.

4. Assume that UE is not allowed to short sell. How should UE construct its risky portfolio?

Refer to this portfolio as P2. How costly is the short sale constraint? (Note: Continue to

assume that UE uses the historical averages to proxy for expected returns.)5. The CFO is also considering managing the risky portfolio passively. After finding out the

market capitalisation of each asset category, you determine that the weights for the passive

portfolio are as follow:

ISF: 1.23%

IXUS: 32.27%

BND: 40.98%

VOO: 14.02%

IYR: 11.23%

GBTC: 0.27%

Refer to this portfolio as P3. Use P3 to calculate the expected return of each asset category

implied by the market, assuming that the market return is 0.7% per month. After examining

the implied expected returns, you and your colleagues believe that some adjustments are

necessary. Since central banks around the world are raising interest rates, your team believes

that the expected return for BND should be adjusted downward by 0.02% per month. You

also believe that blockchain technology will quickly become more important, so the

expected return for GBTC should be increased by 0.01% per month. Form an active portfolio

that incorporate these views and refer to it as P4. Calculate the weights for P4.

6. A nonprofit organisation, UE is very concerned about its investment risk. Suppose UE uses

the variance-covariance method (with normality assumption) and data from 2016 to 2020 to

estimate VaR. What is the VaR of monthly return on P4?

7. The CFO wants to ensure that the standard deviation of the risky portfolios monthly return

does not exceed 0.03, and the one-month 99% VaR does not exceed 6%. Use the expected

returns derived in Q5 (i.e., those that incorporate your own view) to construct the optimal

risky portfolio under these risk management constraints while assuming short sales are not

allowed. Refer to this portfolio as P5 and calculate its weights. (Note: When calculating the

VaR, use the expected returns derived in Q5 for consistency.)

8. Compare the performance of P1 ~ P5 using data from January 2021 to August 2022.

Deliverable:

Write up a report that answers all the above questions. Make sure the results are logically presented.

You should begin by briefly introducing the purpose of this report. Next, provide detailed

explanations on your data, methods, numerical results, and result discussions. Lastly, the

conclusion section should provide a summary of your recommendations on how UE should invest.

Feel free to add additional sections. Your report should not exceed 3,000 words (tables, references,

and appendices are not included in the word count). Each group should upload one PDF file to

BART. Other forms of document (e.g., Excel worksheet) will not be accepted.Optional:

If you wish to earn extra credits, consider incorporating some of the following into your analysis:

9. Estimate VaR using other methods. Compare the estimation results with those of the variance

covariance method. Are there huge differences? Why or why not? Do you recommend UE to

change its VaR estimation method? How do these changes affect portfolio weights?

10. Does the problem of measurement error in expected returns and the covariance matrix affect

your results? Provide evidence to support your argument.