# Thread: Sample CFA Level 2 question bank for June 2013 exam

1. Originally Posted by rahuldaga89
See girl, I doubt there is anything major to explain in q# 2 and #4.Its plain theory.
I'll write heteroskedasticity = HSK ; serial correlation = SC & multicollinearity = MCN
#2 - Breusch- Pagan test is used for HSK and Durbin Watson test is used for SC.
[and if u ask me to explain this , I doubt you've read Quant and if you have not, you surely dont read further. Surely I'm not being rude. Just doubtful.]
#4 - I am simply copying the content of the question.
"To correct HSK, we use White corrected standard error and replace the standard error of independent variable with that error and again conduct a t-test using the original regression coefficient."
"SC can be correcting by adjusting the specification of the model by incorporating a seasonal term.
For correcting MCN, one or two independent variables can be omitted from the original regression equation and the regression can be conducted again."

q# 6 - In both HSK & positive SC, standard errors terms tends to be small (not always, but general case in economic and financial data) which makes computed t-stats to be larger than usual and therefore we reject null hypothesis very often incorrectly, even when null is actually true. And this is what we call type 1 error - Rejecting ture null incorrectly.
In MCN, the case is almost opposite. The standard errors of the affected coefficients tend to be large. In that case, the test of the hypothesis that the coefficient is equal to zero may lead to a failure to reject null hypothesis, which is actually false. That what we call a type 2 error.

Q#3 -
HSK Check - n*R^2 from the regression of residuals = 50*.032 = 1.6 which is less than Critical Chi-square value 3.841. So we dont reject the null that there is no HSK.
SC Check - DW stat is between dl & du , that means its inconclusive. So cant answer in favor of SC.
MCN Check - None of the individual coefficients significantly differ from zero due to higher p-value than .05 . But R-square is 74.67% , that means all coefficients together explain much of variation but not individually. Ideal condition for MCN.

p.s. - If u still need more explanation, drop me a PM.

Hey Rahul,

Thanks a lot for explaining the answers. Ya, m a bit weak in Quant

Will drop PM, if I need any further clarifications.

Thanks,
Nidhi.

1. a
2. b
3. b
4. c
5. c
6. a

3. Solutions to Item set for 21-March:

1. Correct Answer is A: B270 = 1- (0.04*270/360) = 1-0.03 = 0.97. B180 = 1 – (0.035*180/360) = 1-0.0175 = 0.9825. Futures price = B270/B180 = 0.97/0.9825 = 0.9873.
2. Correct Answer is C: Yes, arbitrage profit is possible as the no-arbitrage price is different than the market price. We will sell the futures contract and buy T-bill with 270 days to expiry and sell T-bill with 180 days to expiry. Total arbitrage profit after 270 days= (0.9910-0.9873)*\$1,000,000*(1/0.9873) = \$3,770.53.
3. Correct Answer is A: If the current market T-bill futures price is lesser than the no-arbitrage price, we will take long position in the futures position and short the longer maturity T-bill and go long on shorter maturity T-bill.
4. Correct Answer is C: Futures price of bond with a delivery option = [Bond price*(1+rf)T – FVC]*(1/CF) = [121.5*(1+0.05)1.25 – (4*1.050.75 + 4*1.050.25)]*(1/1.18) = \$102.49.
5. Correct Answer is B: The forward prices are lower when there is a positive correlation between the interest rates and the underlying asset. Mark-to-market feature is preferred in that case.
6. Correct Answer is B: Rahul is not correct regarding backwardation. The backwardation occurs when the benefits of holding the asset exceed the opportunity cost plus additional holding costs.

4. Item set for 22-March (Derivatives):

David Bob Case Scenario

David Bob, CFA, is a derivatives analyst at Capital Inc. Capital Inc. deals mainly in arbitrage positions along with leveraged positions. David is following the options prices and futures prices of a company, Slyfly Limited. Because of the low liquidity and trading in this script, there are good chances to find arbitrage opportunities.

The prices for the Slyfly Limited are given in Exhibit 1.

Exhibit 1
Slyfly Limited

 Call price (Exercise price = \$25) \$3.8 Put price (Exercise price = \$25) \$1.0 Futures price \$27.50 Annual risk-free rate 5.0% Days to expiry 180 days

The days to expiry in Exhibit 1 are same for both the option contracts and futures contract.

David identifies the arbitrage opportunities in the company and takes the position accordingly. He is worried about the increase in competition as markets are becoming more efficient. Because of the efficiency in the market, there are very less arbitrage opportunities available. Even when few opportunities are available, it does not make economic sense to take position into those due to high transaction cost and impediment to borrowing the funds at risk-free rate.

David wants to learn about the Greeks in options so that he can use those in taking other kind of positions in the derivatives markets and can provide value to his clients. He attends a program by the research head of the company, Jim Carbon.

Jim Carbon explains about the Greeks involved with options. He gives the following statements:

Statement 1: The gamma is larger when there is more uncertainly about whether the option will expire in- or out-of-the-money.
Statement 2: Thetas are positive when the put is deep-in-the money, the volatility is high, the interest rate is low, and the time to expiration is low.
Statement 3: The rho has more impact when the underlying is an interest rate rather than equity.
Statement 4: The gamma is maximum for at-the-money options and is similar to duration in the fixed income securities.

David is concerned about one portfolio of his client. The client wants to secure his portfolio value by dynamic delta hedging. The client has 1,000 shares of a stock in his portfolio and the put delta of the stock is -0.4. David explains to him that the portfolio value can also be secured via options. By selling a call option and buying a put option, a zero cost condor can be created and that can secure the portfolio value with no cost at all.

He also explains that in delta hedging, with the movement in the underlying, the portfolio position needs to be rebalanced and there will be more transaction charges involved. But the client is adamant about the delta hedging and doesn’t want to take condor position.

1. What is the no-arbitrage futures price as per the data given in Exhibit 1?
a) \$27.21
b) \$27.39
c) \$27.73

2. What is the total arbitrage possible if you are allowed only to take one contract?
a) \$0.29
b) \$0.36
c) \$0.52

3. What is the position taken by David in the option and futures contracts to make arbitrage profit in Slyfly Limited?
a) Short position in call option and a zero-coupon bond with exercise price as the par value; long position in put option and the futures contract
b) Long position in call option and a zero-coupon bond with exercise price as the par value; short position in put option and the futures contract
c) Long position in call option and a zero-coupon bond with exercise price as the current value of the bond; short position in put option and the futures contract

4. Which of the statements made by Jim Carbon are most likely to be accurate?
a) Statement 2, 3 and 4
b) Statement 1 and 3
c) Statement 3 and 4

5. Thetas are positive when
a) The put is deep in-the-money, the volatility is low, the interest rate is high, and the time to expiration is high
b) The put is deep-in-the money, the volatility is high, the interest rate is low, and the time to expiration is low
c) The put is deep in-the-money, the volatility is low, the interest rate is high, and the time to expiration is low

6. What is the position take by David in the put options for securing the portfolio value by the delta hedging?
a) Short position in 400 put options
b) Short position in 2,500 put options
c) Long position in 2,500 put options

5. Solutions to Item set for 22-March:

1. Correct Answer is C: The no-arbitrage futures price = (C0 – P0)/(1+Rf)T + X = (3.8-1.0)/1.05180/365 + 25 = \$27.73.
2. Correct Answer is B: The put-call parity equation for a futures contract is: C0 + X/(1+Rf)T = P0 + FT/(1+Rf)T. The value of left hand side of the equation is \$28.20 and the value of the right hand side is \$27.84. Total arbitrage profit equals 28.20 – 27.84 = \$0.36.
3. Correct Answer is A: To make arbitrage profit, David took long position in the right hand side of the equation and short position in the left hand side of the equation.
4. Correct Answer is B: Statements 1 and 3 are correct. Statement 2 is wrong as explained in the question 5. Statement 4 is wrong because the gamma is similar to the convexity (second derivative) in the fixed income securities rather than duration.
5. Correct Answer is C: Thetas are positive when the put is deep-in-the money, the volatility is low, the interest rate is high, and the time to expiration is low.
6. Correct Answer is C: In case of put delta, the position will be similar to the position in the underlying. So, the position will be long and the total options needed to be bought = 1,000/0.40 = 2,500.

6. Item Set for 23-March (Equity):

Arjun Gupta Case Scenario

Arjun Gupta is a CFA level II candidate. He is doing valuation for a company, Tram International. Tram International is an airline company and has been into the business for a considerable period of time. The company is currently not paying a dividend but is expected to pay a dividend after 5 years on a regular basis. An excerpt from the company’s Management Discussion & Analysis has been given in the Exhibit 1.

Exhibit 1
MD&A

 The company is growing at a considerable rate. The growth rate is expected to slow down in coming years because of competition and business scenario. We are committed to do good for our shareholders. We have decided to pay dividends after 5 years. The dividend payout ratio will be kept constant at 50% forever so that sustainable growth can be fueled by the retained earnings.

The management of the company has been accurate and credible in its forecasts in previous years. They have been successful in implementing everything said by them. The company’s earnings growth rate was 18% in the concluding year. The management thinks that the earnings growth rate of the company will fall from 18% to 8% linearly at a rate of 2% per annum in next 5 years. After 5 years, the growth rate is expected to remain constant at 8% per annum.

Exhibit 2
Tram International

 Earnings per share \$5.00 Target D/E ratio 0.667 WACC 10.0% Before-tax cost of debt 10.0% Marginal tax rate 40.0% Beta 1.2 Market risk premium 5.0%

Arjun shows his valuation to his manager, Thomas. Thomas asks that why the company is not paying the dividend from the next year.

Arjun: The Company is currently in the high growth phase. It is going to use all of the retained earnings to fuel that growth. That’s why it would not pay a dividend in next 5 years. After 5 years, the earnings growth rate would subside and the company would need less retained earnings and then it can pay the dividends.

Thomas: So, the company is trading off growth with dividend payouts.

Arjun: Yes. It is beneficial for the stockholders that company reinvests its money if the company has good opportunities to invest and can earn higher ROE than the required rate of return.

Thomas: What are the factors that contribute to the ROE?

Arjun: The profit margin, asset turnover and financial leverage affect the ROE. The higher the value of those factors, the higher is the ROE. For a company, the ROE is higher than the required rate of return in the initial growth period and it eventually subsides to the level of required rate of return.

Thomas: What will happen if the ROE falls below the required rate of return by equity holders?
Arjun: The net income of the company will become negative in that case.

1. Which dividend discount model is the most appropriate model for valuing Tram International?
a) Gordon growth model
b) Two stage dividend discount model
c) H-model

2. What is the cost of equity for Tram International?
a) 11.00%
b) 12.67%
c) 18.00%

3. What is the value of the company per share using dividend discount model?
a) \$56.08
b) \$61.27
c) \$93.98

4. Is the statement made by Arjun that the net income of the company would become negative when ROE is less than required rate of return by equity holders, correct?
a) Yes
b) No
c) Can’t say

5. When the company would start the payment of dividends, what percentage of required return will be provided by the dividend yield?
a) 36.84%
b) 50.00%
c) 63.16%

6. What would have been the value of the stock if the company has planned to start the dividend payout from the next year and managing the exact same growth rate in earnings?
a) \$66.97
b) \$68.79
c) \$77.68

7. Solution for 23rd March

1. A
2. C
3. B
4. B
5. A
6. C

8. Solutions to Item set for 23-March:

1. Correct Answer is A: The dividend of the company is expected to grow at a constant rate from its initiation. The Gordon growth model is the most appropriate model for valuing Tram International.
2. Correct Answer is B: Cost of equity = [WACC – wd*rd*(1-t)]/we = (0.10 – 0.40*0.10*0.60)/0.60 = 12.67%.
3. Correct Answer is A: Earnings per share after 5 year = 5*1.16*1.14*1.12*1.10*1.08 = 8.79. Earning in the 6th year = 8.79*1.08 = 9.50. Dividends in the 6th year = 0.5*9.50 = 4.75. Value per share = {4.75/ (0.1266-0.08)}/ (1+0.1266)5 = \$56.08.
4. Correct Answer is C: The net income will become negative only if the company is not able to pay its debt holders from the earnings. Economic income will be negative in case ROE is less than the required return on equity. The accounting net income can be anything.
5. Correct Answer is C: The return provided by the growth factor = 8%. The return provided by the dividend yield = (0.1266-0.08)*100 = 4.67%. Percentage of return provided by the dividend yield = 4.67/12.67 = 36.84%.
6. Correct Answer is B: The Company will pay a dividend of 2.90, 3.31, 3.70, 4.07 and 4.40 in next 5 years. The sum of present value of those payments= 12.72. Adding this to the value obtained in the question 27 to get the share price as \$68.79

9. Item set for 24-March (Derivatives):

Moe Greene Case Scenario

Moe Greene is a manager at Vegas Inc. Vegas Inc. is a U.S. based company and is into casinos business. It is planning to open casinos in Japan. It needs to borrow JPY 500 million (Japanese Yen) from the market for its operation. The company finds a party which is ready to enter into a swap contract with it.

The current exchange rate and the interest rates in USD denominated loans are given in Exhibit 1.

Exhibit 1

Current exchange rate 92 JPY/USD
180-days LIBOR 3.50%
360-days LIBOR 3.80%
540-days LIBOR 4.20%
720 days LIBOR 4.50%

The interest rates in Japanese denominated loans are given in Exhibit 2.

Exhibit 2
180-days interest rate 1.20%
360-days interest rate 1.50%
540-days interest rate 1.70%
720-days interest rate 2.00%

The parties enter into a fixed-fixed currency swap with a notional principal of JPY 500 million. The term for the swap is two years and the interest rates are paid semi-annually.

After 450 days the interest rates in dollar denominated loans and JPY denominated loans change. The changed rates are given in Exhibit 3.
Exhibit 3
LIBOR JPY interest rate
90 days 5.20% 2.10%
270 days 6.00% 2.30%

The exchange rate after 450 days is 88 JPY/USD. The exchange rate at the end of the swap contract (after 720 days) is 90 JPY/USD.

Moe Greene also looks at the transactions which the company is expected to make and the revenues that the company is expected to receive in the future. The company is expecting a net liability exposure of floating rate securities having worth \$100 million after 1 year. The average duration for the floating rate securities is 4 years. The company wants to lock in the fixed rate after 1 year (when the liabilities will arise) if the fixed rate is lesser than the floating rate. So, Moe Greene decides to enter into the swaption contract.

Michael Corleone, another analyst at the company, asks Moe about how to terminate a swap contract using a swaption and the properties of swaption.

Moe Greene states the following:
Statement 1: If the swap is pay fixed-receive floating, then the swap can be terminated by entering into a payer swaption.
Statement 2: If the swap is pay floating-receive fixed, then the swap can be terminated by entering into a payer swaption.
Statement 3: In the swaption, both parties have the obligation to enter into the underlying swap contract.
Michael also asks Moe about the credit risk in a swap contact.

Moe Greene: The credit risk in swaps is relatively higher. The party which has a positive value of swap has a credit risk exposure that the counterparty does not pay the swap value. It can be reduced by the netting. The credit risk is usually higher at the middle of the swap contract.

1. What are the swap rates for the dollar denominated loan and the JPY denominated loan in the swap?
a) 4.12% and 1.64% respectively
b) 4.25% and 1.80% respectively
c) 4.34% and 1.96% respectively

2. What is the swap value for Vegas Inc. after 450 days?
a) \$210,917.10
b) \$265,776.5
c) \$323,792.8

3. What is the value of swap for Vegas Inc. at the end of 720 days?
a) \$57,384.4
b) \$120,772.9
c) \$210,917.1

4. What is the swaption taken by Moe Greene?
c) 1X5 payer swaption

5. Which of the following statements made by Moe Greene about the swaptions are correct?
a) Statement 1 and 3
b) Statement 1 only
c) Statement 2 only

6. Which of the following swap contracts is most likely have a higher credit risk near the end of the contract?
a) Equity swap contract
b) Interest rate swap contract
c) Currency swap contract

10. Solutions to Item set for 24-March:

1. Correct Answer is C: Swap rate for dollar denominated loan = (1-z4)/ (z1+z2+z3+z4). z1=1/ (1+0.0350*180/360) = 0.9828. z2 = 1/ (1+0.038*360/360) = 0.9634. z3= 1/ (1+0.042*540/360) = 0.9407. z4=1/ (1+0.045*720/360) = 0.9174. Swap rate = 0.0217*360/180 = 4.34%.
For JPY denominated loan, z1=1/ (1+0.012*180/360) = 0.9940. z2=1/ (1+0.015*360/360) = 0.9852. z3=1/ (1+0.017*540/360) = 0.9751. z4= 1/ (1+0.02*720/360) = 0.9615.Swap rate = 0.0098*360/180 = 1.96%.
2. Correct Answer is B: Semi-annual coupon for dollar-denominated bond = 0.0217*500,000,000/92 = \$117,955. Semi-annual coupon for JPY denominated loan = JPY500, 000,000*0.009822= JPY 4910907. The value of dollar denominated bond = 117,955/ (1+0.052*90/360) + (500,000,000/92 + 117,955)/ (1+0.06*270/360) = \$5,430,066. The value of JPY denominated loan = 4,910,907/ (1+0.021*90/360) + (500,000,000 + 4,910,907)/ (1+0.023*270/360) = JPY501, 234,149 = \$501,234,149/88 = \$5,695,842.5. The value of swap to the company = 5,695,842.5 – 5,430,066 = \$265,776.5.
3. Correct Answer is A: At the end of the contract, the USD loan party has to pay \$500,000,000/92 + \$117,955 = \$5,552,738.2. The JPY loan party has to pay = JPY500, 000,000 + JPY4, 910,907 = JPY504, 910,907 = \$5,610,121.6. The value of swap to the company = 5,610,121.6 – 5,552,738.2 = \$57,383.4.
4. Correct Answer is C: The Company has a net liability exposure for floating interest rate payment i.e. it is floating rate payer. To lock-in the maximum fixed rate, the company can enter into the 1X5 payer swaption i.e. the company has the option to enter into the swap as the fixed rate payer and receive the floating rate.
5. Correct Answer is C: Statement 2 is correct.
6. Correct Answer is C: The currency swap contract is most likely to have a higher credit risk at the end of the contract because the most of the credit risk arises due to the change in the exchange rate.