Question

You decide to invest $100,000 in cryptocurrencies and you use that amount to buy bitcoin. Your bitcoin appreciate by 30% in one month, at which point you liquidate half your position for cash, which you do not reinvest. Bitcoin appreciates by another 25% during the second month and you sell an additional 40% of your holdings. The cryptocurrency then falls by 60% in the third month, at which point you liquidate your entire position for cash.

a. What is your dollar weighted monthly return?

b. What is the effective annualized return of your answer to part a. above?

c. What would have been your monthly return had you not liquidated any portion of your position until the end of the third month?

Answer 1

Investment in Bitcoin : 100000

a. Dollar weighted monthly return : w1 * i1 + w2 *i2 + w3 *i3

Where w denotes the weights and i denote the return in the period.

w1 = 50 %

w2 = 40 %

w3 = 10 %

i1 = 30 %

i2 = 25%

i3 = -60%

Weighted average return

( 50%*30* ) + ( 40%*25* ) + (10%*-60%)

15 + 10 - 6 = 19 % Weighted Average Return

B: Formula to Compute Effective Annualized return (EAR) is

EAR = (1+i/n)ⁿ - 1

where i is interest rate and n is no of periods for which compounding is done.

our i is 19 % as calculated above

Putting values in formula we get.

(1+0.19/3)³ - 1

1.2022 - 1

0.2022 or 20.22 % is EAR

C. To get the monthly return, first we need to get the value of the portfolio at the end of three months.

Loss of Capital = Closing Balance - Initial Balance

= 65000 - 100000

-35000 = Loss

Return on Investment =( Profit/Loss of Capital / Invested capital )* 100

ROI = (35000 / 100000)*100

ROI = 35 %

This ROI is for a period of three months, we will divide it by three to get our monthly ROI.

Monthly ROI is 35 / 3 = - 11.66 %