answers for 19th march
b
a
c
c
a
b
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You can do anything You set your mind to !!!
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You can do anything You set your mind to !!!
Sol to March 19th:-
1. b
2. c
5. a
6. b
Solutions to Item set for 19-March
1. Correct Answer is B: Adjusted R2 = 1- {(n-1)/ (n-k-1)}*(1-R2) = 1 – (49/46)*(1-0.7467) = 0.7301.
2. Correct Answer is A: BP test is used for heteroskedasticity and DW test is used for serial correlation.
3. Correct Answer is C: Heteroskedasticy and serial correlation is not present as it can be seen clearly from the test results of the Exhibit 2. Mulitcollinearity is present because no t-statistic is statistically significant but the F-test statistics is statistically significant.
4. Correct Answer is C: All the correction methods specified by Vinod Jayakumar are correct.
5. Correct Answer is A: Predicted P/E = 5.35 – 0.32*dividend payout + 12.5*earnings growth rate – 0.60*beta = 5.35 – 0.32*0.60 + 12.5*0.08 – 0.60*1.2 = 5.438.
6. Correct Answer is B: Heteroskedasticity and serial correlation lead to too many Type I errors and multicollinearity leads to too many Type II errors.
Item set for 20-March (Derivatives):
Pallavi Jain Case Scenario
Pallavi Jain, CFA, is working in Citibank as interest rate analyst. She deals in forward rate agreements. The company needs a loan worth $2 million for 6 months after 3 months. She looks at the various interest rates for different periods. The company wants to book loan at the current forward rate implied by the interest rates. The interest rates are given in Exhibit 1.
Exhibit 1
Interest Rates at the beginning of the contract
90 days 3.5% 180 days 4.0% 270 days 4.5% 360 days 5.0%
She enters into the forward rat agreement on the behalf of company. After 30 days the interest rate in the market changes. The interest rates after 30-days are given in Exhibit 2.
Exhibit 2
Interest rates after 30-days of the contract
60 days 4.0% 150 days 4.5% 240 days 5.0% 330 days 5.5%
The interest rates after 90-days i.e. end of the forward rate of agreement are given in Exhibit 3.
Exhibit 3
Interest rates at the end of forward rate agreement
90 days 5.0% 180 days 5.5% 270 days 6.0% 360 days 6.5%
Pallavi’s manager Tejal Joshi asks her about whether there was any other way to lock in the interest rates apart from FRA. Pallavi replies that interest rate can also be locked in by using swaptions.
Tejal: What is the difference between hedging via swaptions and hedging via forward rate agreement?
Pallavi: In forward rate agreement, we don’t have to pay a premium but in swaption we have to pay a premium. Also, in case of forward rate agreement, our interest rate is locked in a way that we have to pay that much interest. While in case of swaption, we may have additional benefit of paying lower interest rate than the locked in interest if the swaption expires worthless.
Pallavi was researching forward market for fixed income securities. She found out that very forward contracts are underpriced in the market and few are overpriced in the market. She went straight to her manger and informed her about opportunity to make arbitrage profit.
Her manager asks her about the credit risk of the forward position and also the relation between the market value of forward contract and the credit risk amount.
Pallavi: Any party long or short can have credit risk. The party which is in loss bears the credit risk. The credit risk amount is generally lesser than the market value of the contract.
1. What is the interest rate at which the company locked in the loan?
a) 4.46%
b) 4.72%
c) 4.96%
2. What is the value of forward rate agreement to the company after the end of 30 days?
a) $3,303.71
b) $3,413.84
c) $3,527.63
3. What is the total profit realized by the company at the end of forward rate agreement contract?
a) $4,672.91
b) $5,288.28
c) $5,433.70
4. Which of the statement made by Pallavi Jain is least accurate about the difference between swaption and forward rate agreement?
a) Statement regarding the inflexibility of forward rate agreement about the locked-in interest
b) Statement regarding the possibility of lower interest rate in case of swaption
c) All the statements made by her are correct
5. Which of the following arbitrage would be done in case when the forward contract is underpriced?
a) Cash and carry arbitrage
b) Reverse cash and carry arbitrage
c) Either of the above
6. Which of the statements made by Pallavi is most accurate about the credit risk?
a) About which party can have the credit risk
b) About which party bears the credit risk
c) About the relation between the credit risk amount and market value of the forward contract
@Rahul Daga:- Please explain the solutions for Q# 2, 3, 4 and 6 of 19th. I am not clear abt it. Almost all of urs answers are correct :-)
Cheers,
Nidhi.
Last edited by Nidhi Taleja; 20-03-2013 at 11:59 PM.
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.
Last edited by rahuldaga89; 21-03-2013 at 11:01 AM. Reason: typo
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You can do anything You set your mind to !!!
Solutions to Item set for 20-March:
1. Correct Answer is C: The Company will buy a 3X9 FRA. The price of 3X9 FRA = [{(1+0.045*270/360)/(1+0.035*90/360)}-1]*(360/180)= 4.9566%
2. Correct Answer is A: After 30 days, the price of new FRA = [{(1+0.05*240/360)/ (1+0.04*60/360)}-1]*(360/180) = 5.298%. The value of FRA = (0.05298 – 0.049566)*(180/360)*2,000,000/ (1+0.05*240/360) = $3,303.71.
3. Correct Answer is A: Total profit at maturity = (0.055-0.04966)*(180/360)*2,000,000/ (1+0.055*180/360) = $5,288.28.
4. Correct Answer is C: All the statements made by Pallavi regarding the difference between swaption and forward rate agreement are correct.
5. Correct Answer is B: The forward contract is underpriced. So, for arbitrage, that needs to be bought and the spot instrument needs to be sold. It is done in reverse cash and carry arbitrage.
6. Correct Answer is A: Any party can have a credit risk. The party in the profit bears the credit risk. The credit risk amount is equal to the market value of the forward contract.
Item set for 21-March (Derivatives):
Rahul Daga Case Scenario
Rahul Daga is a derivative trader. He mainly takes position in futures contracts. He trades all kinds of products ranging from Treasury bills to commodities. Most of his profits come from the arbitrage positions. Generally, markets are not that efficient and there are plenty of arbitrage opportunities available. He is looking at the Treasury bills futures for the arbitrage. The current market prices are given in the Exhibit 1.
Exhibit 1
Treasury Bills
Days to expiration Quoted at a discount of 180 days 3.5% 270 days 4.0%
The 90-days T-bill futures contract which has 180 days to expiry is currently trading at 0.9910.
Rahul has also taken a long position in the futures contract of a bond with a delivery option. The conversion factor for the bond is 1.18. The bond is a semi-annual coupon paying bond. The coupon rate is 8% per annum. The risk-free rate is 5.0% per annum. The futures contract has 15 months to expiry and the bond has just paid a coupon. The bond is trading at $121.5 and has a face value of $100.
He looks at the forward prices and futures prices of the same underlying instrument with the same expiry period. He finds out that the forward prices are lower than the futures prices. But the difference is very small.
Rahul always finds it difficult to make the riskless arbitrage in Eurodollar contracts. This is due to the fact that the Eurodollar futures is structured like a T-bill contract as though the underlying were a discount instrument while the Eurodollar spot is an add-on instrument. Due to mismatch in the design of spot and futures instrument, it is difficult to use Eurodollar contract as a hedging instrument.
In the commodities market, the expected spot price of the oil is greater than the futures price and the spot price is lesser than the futures price. Rahul tells his colleague that the oil contract is in normal backwardation and also in contango.
His colleague asks him what the reason behind the futures contract to be in backwardation. Rahul explains that when the benefits of holding the assets are less than the opportunity cost of holding the assets plus the additional holding costs, then the contract comes into backwardation.
His colleague asks him about the benefits of holding an asset. Rahul tells that there can be two kinds of benefits: Monetary and Non-monetary benefits.
The monetary benefits include dividends, coupons etc. The non-monetary benefits include convenience yield. Convenience yield means that the holder of an asset is benefiting from holding the asset. It is subjective. An example could be the gold as an underlying instrument. The holder can use it as ornaments for the period of the contract. Similarly, if a machine is hold as an underlying asset, it could be used by the holder.
His colleague: What is the main difference between the forward and futures contract considering the risk as a basis?
Rahul: The forward contracts have more credit risk and the futures contracts have almost zero credit risk. The futures contracts have almost zero credit risk because of marked to market feature. They are daily marked to market. Because of which the losing position generally doesn’t default as the total movement in a day is quite less. The clearinghouse acts as an counterparty and they demand some margin amount in your account. So, the chances are default is extremely low.
1. What is the no-arbitrage price of the T-bill futures contract which has 180 days to expiry?
a) 0.9873
b) 0.9892
c) 0.9910
2. Is there any arbitrage possible in the T-bill futures contract? If yes, then how much profit can be made at the end of 270 days from today?
a) No arbitrage profit is possible
b) Yes, $3,756.45
c) Yes, $3,770.53
3. If the current market T-bill futures price is lesser than the no-arbitrage futures price, then what transactions should be done to make arbitrage profit?
a) Long T-bill futures, short longer maturity T-bill, long shorter maturity T-bill
b) Long T-bill futures, long longer maturity T-bill, short shorter maturity T-bill
c) Short T-bill futures, long longer maturity T-bill, short shorter maturity T-bill
4. What is the no-arbitrage futures price for the bond with a delivery option?
a) $98.89
b) $102.49
c) $102.66
5. What is the most likely reason for the difference between the forward price and the futures price?
a) The correlation between the interest rates and the underlying asset is zero
b) The correlation between the interest rates and the underlying asset is positive
c) The correlation between the interest rates and the underlying asset is negative
6. Which of the following statement made by Rahul is least accurate?
a) Regarding contango and normal backwardation
b) Regarding backwardation
c) Regarding credit risk of the contracts
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