Practice 50 CFA Level I Derivatives & Alternative Investments calculation questions with answers and detailed explanations. Work through CFA-style problems, review step-by-step solutions, and strengthen your understanding of derivatives pricing, forwards, futures, options, swaps, alternative investment concepts, and essential investment calculations.
Theresa, an investment manager, anticipates that the price ofa particular underlying, cur- rently selling at $64, is going to increase in value over the next three months. She purchases a call option expiring in three months on the underlying. The call option has an exercise price of $68 and sells for $5.
If the price of the underlying is $71 in three months, Theresa’s profit is:
Answer
B. -$2.
Explanation
Step 1: Value at expiration = max(0, S_T – X)
Value at expiration = max(0, $71 – $68) = $3
Step 2: Profit = c_T – c_0
Profit = $3 – $5 = -$2
Answer
C. $0.
Explanation
Step 1: Value at expiration = max(0, S_T – X)
Value at expiration = max(0, $73 – $68) = $5
Step 2: Profit = c_T – c_0
Profit = $5 – $5 = $0
Answer
B. $4.
Explanation
Step 1: Value at expiration = max(0, S_T – X)
Value at expiration = max(0, $77 – $68) = $9
Step 2: Profit = c_T – c_0
Profit = $9 – $5 = $4
A bond with a face value of $1,000 is selling for $965. A call option selling for $6 has an exercise price of $1,025. Consider the following questions about a covered call if the price of the bond at expiration is $960.
The value at expiration for the buyer is:
Answer
B. $960.
Explanation
V_T = S_T – max(0, S_T – X)
V_T = $960 – max(0, $960 – $1,025)
V_T = $960 – $0 = $960
Answer
B. $1.
Explanation
Profit = V_T – (S_0 – c_0)
Profit = $960 – ($965 – $6) = $1
Answer
C. $959.
Explanation
S_T* = S_0 – c_0
S_T* = $965 – $6 = $959
Answer
C. $6.
Explanation
When the balance in the margin account falls below the maintenance margin, Robert must deposit funds to return the balance to the initial margin requirement. Therefore, the variation margin is $9 – $3 = $6.
Answer
C. $12 million.
Explanation
Minimum hedge fund size = Minimum investment size/Maximum percentage of a fund $80 million = Minimum investment size/0.15
Minimum investment size = $12 million
A call option is selling for $3 and has an exercise price of $19. Assume the price of the
underlying at expiration is $23.
The value at expiration for the buyer is:
Answer
B. $4.
Explanation
Value at expiration = max(0,S_t – X)
Value at expiration = max(0,$23 – $19) = $4
Answer
A. $1.
Explanation
Profit = c_T – c_0
Profit = $4 – $3 = $1
Answer
C. infinity, $3.
Explanation
Maximum profit to the buyer = infinity
Maximum loss to the buyer = $3
Answer
C. $16.36.
Explanation
Forward price = S_0(1 + r)^T
$16.52 = S_0(1.04)^(3/12)
S_0 = $16.36
A call option is selling for $5 and has an exercise price of $27. Assume the price of the underlying at expiration is $25.
The value at expiration for the buyer is:
Answer
A. $0.
Explanation
Value at expiration = max(0, S_T – X)
Value at expiration = max(0, $25 – $27) = $0
Answer
B. -$5.
Explanation
Profit = c_T – c_0
Profit = $0 – $5 = -$5
Answer
B. $0.
Explanation
The call option is out-of-the-money because the strike price ($22.00) exceeds the market price ($21.50). Therefore, the value of the option is $0.
A call option is selling for $6 and has an exercise price of $125. Assume the price of the underlying at expiration is $124.
The value at expiration for the seller is:
Answer
A. $0.
Explanation
Value at expiration = -max(0, S_T – X)
Value at expiration = -max(0, $124 – $125) = $0
Answer
C. $6.
Explanation
Profit = -c_T – c_0
Profit = -$0 + $6 = $6
A call option is selling for $3 and has an exercise price of $86. Assume the price of the underlying at expiration is $91.
The value at expiration for the seller is:
Answer
A. -$5.
Explanation
Value at expiration = -max(0, S_T – X)
Value at expiration = -max(0, $91 – $86) = -$5
Answer
B. -$2.
Explanation
Profit = -c_T – c_0
Profit = -$5 + $3 = -$2
Alpha Hedge Fund invests $50 million in each of Gamma Fund and Delta Fund. Alpha Hedge Fund has a “2 and 20” fee structure. After one year, Gamma Fund is valued at $35 million and Delta Fund is valued at $90 million.
If fees are calculated independently at the end of each year, the total fees charged by Alpha Hedge Fund are:
Answer
B. $7.5 million.
Explanation
Step 1: End of year capital = $35 million + $90 million = $125 million
Step 2: Management fee = ($125 million)(0.02) = $2.5 million
Step 3: Incentive fee = ($125 million – $100 million) (0.20) = $5 million
Step 4: Total fees = $2.5 million + $5 million = $7.5 million
Answer
C. 17.5%.
Explanation
Step 1: End of year capital = $35 million + $90 million = $125 million
Step 2: Management fee = ($125 million)(0.02) = $2.5 million
Step 3: Incentive fee = ($125 million – $100 million)(0.20) = $5 million
Step 4: Total fees = $2.5 million + $5 million = $7.5 million
Step 5: Investment return = ($125 million – $100 million — $7.5 million) /$100 million = 0.175 = 17.5%
Answer
C. $7.0 million.
Explanation
Step 1: End of year capital = $35 million + $90 million = $125 million
Step 2: Management fee = ($125 million)(0.02) = $2.5 million
Step 3: Incentive fee = ($125 million – $100 million – $2.5 million)(0.20) = $4.5 million
Step 4: Total fees = $2.5 million + $4.5 million = $7.0 million
Answer
C. 18%.
Explanation
Step 1: End of year capital = $35 million + $90 million = $125 million
Step 2: Management fee = ($125 million)(0.02) = $2.5 million
Step 3: Incentive fee = ($125 million – $100 million – $2.5 million)(0.20) = $4.5 million
Step 4: Total fees = $2.5 million + $4.5 million = $7.0 million
Step 5: Investment return = ($125 million – $100 million – $7.0 million)/$100 million = 0.18 = 18%
Answer
B. $6.9 million.
Explanation
Step 1: End of year capital = $35 million + $90 million = $125 million
Step 2: Management fee = ($125 million)(0.02) = $2.5 million
Step 3: Incentive fee = ($125 million – $100 million – $3 million)(0.20) = $4.4 million
Step 4: Total fees = $2.5 million + $4.4 million = $6.9 million
Answer
C. Kappa: $0; Zeta: $3
Explanation
The Kappa option is out-of-the money ($0).
The value of the Zeta option is $28 – $25 = $3.
Answer
B. $27.5 million.
Explanation
Minimum hedge fund size = Minimum investment size/Maximum percentage of a fund
Minimum hedge fund size = $5.5 million/0.2 = $27.5 million
Answer
A. $27.22.
Explanation
Forward price = S_0(1 + r)^T
Forward price = $27(1.025)^(4/12) = $27.22
David, an investment manager, anticipates that the price of a particular underlying, currently selling at $184, is going to decrease in value over the next six months. He purchases a put option expiring in six months on the underlying. The put option has an exercise price of $177 and sells for $4.
If the price of the underlying is $190 in six months, David’s profit is:
Answer
C. -$4.
Explanation
Step 1: Value at expiration = max(0, X – S_T)
Value at expiration = max(0, $177 – $190) = $0
Step 2: Profit = p_T – p_0
Profit = $0 – $4 = -$4
Answer
B. -$4.
Explanation
Step 1: Value at expiration = max(0, X – S_T)
Value at expiration = max(0, $177 – $184) = $0
Step 2: Profit = p_T – p_0
Profit = $0 – $4 = -$4
Answer
A. -$1.
Explanation
Step 1: Value at expiration = max(0, X – S_T)
Value at expiration = max(0, $177 – $174) = $3
Step 2: Profit = p_T – p_0
Profit = $3 – $4 = -$1
Answer
B. $3.
Explanation
Step 1: Value at expiration = max(0, X – S_T)
Value at expiration = max(0, $177 – $170) = $7
Step 2: Profit = p_T – p_0
Profit = $7 – $4 = $3
Answer
C. $7.
Explanation
Step 1: Value at expiration = max(0, X – S_T)
Value at expiration = max(0, $177 – $166) = $11
Step 2: Profit = p_T – p_0
Profit = $11 – $4 = $7
Answer
B. $173, $4.
Explanation
Maximum profit to the buyer = X – po = $177 – $4 = $173
Maximum loss to the buyer = $4
A currency is selling for $1.23. A put option selling for $0.12 has an exercise price of $1.27.
Consider the following questions about a protective put if the price at expiration is $1.32.
The value at expiration for the buyer is:
Answer
B. $1.32.
Explanation
V_T = S_T + max(0, X – S_T)
V_T = $1.32 + max(0, $1.27 – $1.32) = $1.32
Answer
B. -$0.03.
Explanation
Profit = V_T – (S_0 + p_0)
Profit = $1.32 – ($1.23 + $0.12) = -$0.03
Answer
A. $0.08.
Explanation
Maximum loss to the buyer = S_0 + p_0 – X
Maximum loss to the buyer = $1.23 + $0.12 – $1.27 = $0.08
Answer
C. Infinity.
Explanation
The maximum profit is unlimited.
Answer
C. $1.35.
Explanation
S_T* = S_0 + p_0
S_T* = $1.23 + $0.12 = $1.35
A bond with a face value of $1,000 is selling for $965. A call option selling for $6 has an exercise price of $1,025. Consider the following questions about a covered call if the price of the bond at expiration is $1,040.
The value at expiration for the buyer is:
Answer
C. $1,025.
Explanation
V_T = S_T – max(0, S_T – X)
V_T = $1,040 – max(0, $1,040 – $1,025)
V_T = $1,040 – $15 = $1,025
Answer
B. $66.
Explanation
Profit = V_T – (S_0 – c_0)
Profit = $1,025 – ($965 – $6) = $66
Answer
A. $66.
Explanation
Maximum profit to the buyer = X – S_0 + c_0
Maximum profit to the buyer = $1,025 – $965 + $6 = $66
Answer
A. $959.
Explanation
Maximum loss to the buyer = S_o – c_o
Maximum loss to the buyer = $965 – $6 = $959
Answer
A. $959.
Explanation
S_T* = S_0 – c_0
S_T* = $965 – $6 = $959
Beta Hedge Fund’s portfolio is valued at $330 million at the beginning of the year. One year later, the portfolio is valued at $412 million. The fund charges a 2.5% management fee based on the end-of-year portfolio value as well as a 20% incentive fee.
If fees are calculated independently at the end of each year, the total fees charged by
Beta Hedge Fund are:
Answer
A. $26.7 million.
Explanation
Step 1: Management fee = ($412 million)(0.025) = $10.3 million
Step 2: Incentive fee = ($412 million – $330 million)(0.20) = $16.4 million
Step 3: Total fees = $10.3 million + $16.4 million = $26.7 million
Answer
B. 16.76%.
Explanation
Step 1: Management fee = ($412 million)(0.025) = $10.3 million
Step 2: Incentive fee = ($412 million – $330 million)(0.20) = $16.4 million
Step 3: Total fees = $10.3 million + $16.4 million = $26.7 million
Step 4: Investment return = ($412 million – $330 million – $26.7 million) /$330 million = 0.1676 = 16.76%
A currency is selling for $16.11. A put option selling for $0.44 has an exercise price of $16.20. Consider the following questions about a protective put if the price at expiration is $15.80.
The value at expiration for the buyer is:
Answer
C. $16.20.
Explanation
V_T = S_T + max(0, X – S_T)
V_T = $15.80 + max(0, $16.20 – $15.80) = $16.20
Answer
A. -$0.35.
Explanation
Profit = V_T – (S_0 + p_0)
Profit = $16.20 – ($16.11 + $0.44) = -$0.35
Answer
B. $0.35.
Explanation
Maximum loss to the buyer = S_0 + p_0 – X
Maximum loss to the buyer = $16.11 + $0.44 – $16.20 = $0.35
Answer
C. Infinity.
Explanation
The maximum profit is unlimited.
Answer
A. $16.55.
Explanation
S_T* = S_0 + p_0
S_T* = $16.11 + $0.44 = $16.55
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