Urgent Finance Assignment

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~ Assess the validity of the various pros and cons of investing in gold discussed iii the ease

Study Questions

The questions below are designed for a course in investments or portfolio management. Alternatively, questions 1-3 and 5-7 could also be used in a first-year MBA. introductory finance course.

1. Watch the WGC presentation on the YouTube weblinl: provided on page 5 of this note. What are the most compelling arguments for and again~~ investing in gold?

2. Using the annual return data for U.S. large cap equities, U.S_ bonds, and gold provided in case E~ibit 2, calculate the mean, standard deviation fQx each asset class, and the cross- correlations for the three asset classes. Given these numbers, which of these asset classes would you be most/least interested in investing. in? Are these results consistent with the WGC's claim of superior risk-adjusted r~~»7is?

3. Again, using the return data. from case Exhibit 2, calculate the annual returns from 1988 to 2011 for three different portfolios' .using the weighted average return formula (i.e., RPorifolio — w~USLargeCap X RUSLa~geC a;~ + W~tUSBonds X RUSBonds ~' w~Gold X RGold~ ~a assuming the portfolio is rebalanced to these weights each year:

• 60% U.S. large cad/4u~i~ U.S. bond

• 50% U.S. large cap/4U% U.S:bondll0% gold

• 34% U.S. large cap,'33% U.S~bondl33%gold

From these returns, cai~~ate the mean and standard deviation of each portfolio. Comparing tl~e portfolios, which one would you prefer and why?

4. How do the t~~eai~s; standard deviations, and correlations calculated from the 1988 to 2011 ann~aai z•e~inz data in case E~iibit 2 compare to those calculated using the June 1992 to J ule 201? ~inonthly return data in case E~ibit 3 for U.S. large cap equities, U.S. bonds; and ~olu? How do you explain the differences and what implications do they have for using Historical data in an optimization?

5. Use the ~iieaizs, standard deviations, and cross-correlations for U.S. large cap equities, U.~. ponds, and gold in case E~iibit 3 (calculated from the June 1992 to June 2012 montli~y data). Using the three-asset mean-variance optimizer given in the spreadsheet,l calculate the optimal portfolio weights and the expected return when the target standard deviation is 10%for two different portfolios:

First, with a portfolio weight of gold fixed at 0%, but the portfolio weights in U.S. bonds and U.S'. large cap are allowed to change.

1 While the 3-asset and 11-asset mean-variance optimizers are provided in the student Excel spreadsheet, the instructor could alternatively ask students to formulate their own.

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• Second, repeat the optimization but allow the portfolio weights of all tii~ree asset classes (LT.S. bonds, U.S. large cap, gold) to change.

The optimal portfolio is the portfolio with the maximum return for. a given level of risk as proceed by the standard deviation. To calculate the weights, use Excel Solves (~r a similar tool). Once you have the Solver dialog box on the screen, you need to identify the following (Figure 1):

Figure 1. Solver parameters.

Solver Paramete s - { +vs 7

Set Objective: portfolioRehirn ',

'.\~ To: ;g~ Max i.`~ Min (7 Value OF.

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PortfolioStr3oev = 7A l TofialPortfnliolAtei9~#=~0%

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Change

Delete

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Q Make Unconstrained Varla6le; Nr n-tJegatve~.

Sele~ a Solvfig Metltod: ~ GRG I I r e.~r ~ ~~ ~e~~s

Solv'v~9 Metfiod _._.... .

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Select fihe G2G Nonlinear er -. ~ e- Solver Problems ffiataresmooth nonlinear. Select the IP Simplex engine fnrl~r,ea- Sdv~r Pr~l ~. d ~eJect tfie Evalu6onary Engine fvr Solver problems that are non-snoofh.

Hdp. l' _ Solve.P

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' Close

a. What is it that you want to maximize? For this example, we wi11 optimize the return of the combined portfolio. To do this, click the "Set Objective" dialog box and then click on: t,ie cell containing the portfolio return. Then, click on the "Max" option.

b. ~~hic11 pai~~l~eters could change in order to maximize the return of the portfolio? Typicali}~ we assume the returns, standard deviations, and correlations of the asset ~~1.3~ses in the optimization are constant and cannot be changed.by the investor. The iiives~o~ iias control over the weights in each asset class. In order to let the optimizer lc~~ow what parameters it can change, click on the "By Changing Variable Cells" option and highlight the two weights (U.S. bonds, U.S. large cap) or three weights (U.S. bonds, U.S. large cap, gold). Unselect the option "Make Unconstrained Variables Non-Negative" to allow for negative weights.

c. What constraints should be placed on the optimized portfolio? First, the weights in the three portfolios should sum to 100% (or equivalently 1.00). To input this constraint, click on the "Add" button. Then input the sum of the three weights on the left-hand side and 100% on the right-hand side. The second constraint is to set the