Instructions

answer questions based on the following information:

In the beginning of the year 2010, Mr. Sanyal had the option to invest Rs. 800000 in one or more of the following assets – gold, silver, US bonds, EU bonds, UK bonds and Japanese bonds. In order to invest in US bonds, one must first convert his investible fund into US Dollars at the ongoing exchange rate. Similarly, if one wants to invest in EU bonds or UK bonds or Japanese bonds one must first convert his investible fund into Euro, British Pounds and Japanese Yen respectively at the ongoing exchange rates. Transactions were allowed only in the beginning of every month. Bullion prices and exchange rates were fixed at the beginning of every
month and remained unchanged throughout the month. Refer to the table titled “Bullion Prices and Exchange Rates in 2010" for the relevant data.
Bullion Prices and Exchange Rates in 2010

Interest rates on US, EU, UK and Japanese bonds are 10%, 20%, 15% and 5% respectively.

Question 99

At the beginning of every month, by sheer luck, Mr. Sanyal managed to correctly guess the asset that gave maximum return during that month and invested accordingly. If he liquefied his assets on 31st December 2010, how much was the percentage gain from his investments?

Solution

To solve this problem, we need to find the maximum possible return Mr. Sanyal could achieve by shifting his entire capital (Rs. 800,000) into the single best-performing asset at the beginning of every month. Each month, the "return" is a combination of that month's accrued interest and the percentage change in the asset's price (bullion) or exchange rate (bonds).
Each monthly multiplier is calculated as the maximum of:
Bullion Yield: $$\frac{\Pr ice\ at\ the\ end\ of\ month}{\Pr ice\ at\ the\ start\ of\ month}$$
Bond Yield:$$\frac{Exchange\ rate\ at\ the\ end\ of\ month}{Exchange\ rate\ at\ the\ start\ of\ month}\times\ \left(1+\frac{Annual\ interest\ rate\ }{12}\right)$$.

Jan: EU Bond -> 1 + (61.5/60 - 1) + 0.20/12 = 1.04167
Feb: EU Bond -> 1 + (62/61.5 - 1) + 0.20/12 = 1.02480
Mar: US Bond -> 1 + (41/41 - 1) + 0.10/12 = 1.00833 (Gold/Silver actually lower)
Apr: UK Bond -> 1 + (72/71 - 1) + 0.15/12 = 1.02658
May: JP Bond -> 1 + (0.54/0.53 - 1) + 0.05/12 = 1.02302
Jun: US Bond -> 1 + (44/42 - 1) + 0.10/12 = 1.05595
Jul: US Bond -> 1 + (45/44 - 1) + 0.10/12 = 1.03106
Aug: US Bond -> 1 + (47/45 - 1) + 0.10/12 = 1.05278
Sep: US Bond -> 1 + (49/47 - 1) + 0.10/12 = 1.05089
Oct: US Bond -> 1 + (50/49 - 1) + 0.10/12 = 1.02874
Nov: JP Bond -> 1 + (0.60/0.59 - 1) + 0.05/12 = 1.02112
Dec: EU Bond (Interest only) -> 1 + 0 + 0.20/12 = 1.01667

1.04167×1.02480×1.00833×1.02658×1.02302×1.05595×1.03106×1.05278×1.05089×1.02874×1.02112×1.01667 $$\approx\ $$ 1.4671.
This amounts to an overall gain of 46.71%