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Question 1Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

If events A and B are mutually exclusive with P(A)=0.30 and P(B)=0.40, what is P(A or B)?

  1. 0.10
  2. 0.58
  3. 0.12
  4. 0.70 Correct answer.

Explanation

For mutually exclusive events, the probability of the union is P(A)+P(B). Since the events cannot occur together, there is no overlap probability to subtract. Adding 0.30 and 0.40 gives 0.70.

Question 2Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

Under the net present value rule, a project with a positive NPV should generally be:

  1. accepted because it adds value Correct answer.
  2. accepted only if payback is short
  3. rejected because it has cash outflows
  4. rejected if IRR is positive

Explanation

NPV discounts expected cash flows at the required return, and a positive NPV means discounted inflows exceed outflows. Accepting such a project increases firm value. Payback and IRR are secondary criteria and do not override a positive NPV for an independent project.

Question 3Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

Which event would most likely shift the demand curve for coffee to the right?

  1. a fall in the price of coffee
  2. higher consumer income for a normal good Correct answer.
  3. a rise in the price of coffee
  4. a decrease in the number of coffee drinkers

Explanation

A rightward shift means consumers demand more coffee at every price. For a normal good, higher consumer income increases demand. A change in the good's own price causes movement along the demand curve rather than a shift.

Question 4Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

The basic accounting equation states that:

  1. equity equals assets plus liabilities
  2. assets equal liabilities minus equity
  3. liabilities equal assets plus equity
  4. assets equal liabilities plus equity Correct answer.

Explanation

The balance sheet identity is Assets = Liabilities + Equity. Assets are resources controlled by the firm, financed by creditor claims and owner claims. Rearranging the identity gives Equity = Assets - Liabilities.

Question 5Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

As the sample size increases, the standard error of the sample mean, holding population standard deviation constant, generally:

  1. increases
  2. becomes equal to population standard deviation
  3. decreases Correct answer.
  4. stays exactly the same

Explanation

The standard error of the mean is sigma divided by the square root of n. As n increases, the denominator increases and the standard error decreases. A smaller standard error indicates a more precise estimate of the population mean.

Question 6Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

A 95% confidence interval for a population mean is calculated as (10.2, 14.8). Which interpretation is correct?

  1. The sample mean has a 95% chance of equaling the true mean.
  2. There is a 95% probability that the population mean lies between 10.2 and 14.8.
  3. About 95% of individual observations lie between 10.2 and 14.8.
  4. About 95% of repeated intervals would contain the true mean. Correct answer.

Explanation

The confidence level describes the long-run coverage of the interval-building procedure. If the study were repeated many times, about 95% of similarly constructed intervals would contain the fixed true mean. Once a specific interval is computed, the parameter is not random.

Question 7Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

A random sample of 20 independent Bernoulli trials has 6 successes. What is the maximum likelihood estimate of the success probability p?

  1. 0.25
  2. 0.60
  3. 0.20
  4. 0.30 Correct answer.

Explanation

For Bernoulli trials, the maximum likelihood estimate of p is the sample proportion of successes. Here the proportion is 6/20 = 0.30. This value maximizes the likelihood of observing exactly six successes in twenty trials.

Question 8Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

A Type I error occurs when:

  1. a true null hypothesis is not rejected
  2. a false null hypothesis is not rejected
  3. a false null hypothesis is rejected
  4. a true null hypothesis is rejected Correct answer.

Explanation

A Type I error is rejecting the null hypothesis when it is actually true. Its probability is the significance level, alpha. A Type II error is failing to reject a false null hypothesis.

Question 9Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

The price of a good rises from $10 to $12, and quantity demanded falls from 20 to 16 units. Using the midpoint formula, the absolute price elasticity of demand is closest to:

  1. 1.00
  2. 1.22 Correct answer.
  3. 2.00
  4. 0.82

Explanation

Midpoint elasticity uses average quantity and average price in the percentage-change denominator. Average quantity is 18 and average price is 11, so elasticity is (4/18)/(2/11) = 1.22. This indicates elastic demand because the value exceeds 1.

Question 10Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

Country A can produce either 10 units of X or 20 units of Y per labor hour. Country B can produce either 8 units of X or 8 units of Y per labor hour. Which statement is correct?

  1. Neither country gains from trade because Country A is more productive in Y.
  2. Country A has comparative advantage in X because it produces more X per hour.
  3. Country A has comparative advantage in X because its opportunity cost is lower.
  4. Country B has comparative advantage in X due to lower opportunity cost. Correct answer.

Explanation

The opportunity cost of one unit of X is 2 units of Y for Country A and 1 unit of Y for Country B. Country B gives up less Y to produce X, so it has the comparative advantage in X. Country A has the comparative advantage in Y.

Question 11Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

Under accrual accounting, revenue is generally recognized when:

  1. the invoice is printed and mailed
  2. the performance obligation is satisfied Correct answer.
  3. the company signs a contract with the customer
  4. cash is received from the customer

Explanation

Accrual accounting recognizes revenue when goods or services are transferred and the performance obligation is satisfied. Cash receipt may occur before or after recognition and does not by itself determine timing. Signing a contract may create obligations but does not necessarily complete performance.

Question 12Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

The risk-free rate is 3%, the expected market return is 8%, and a stock has beta 1.2. According to CAPM, the stock's expected return is:

  1. 9.0% Correct answer.
  2. 6.0%
  3. 9.6%
  4. 8.0%

Explanation

CAPM gives expected return as risk-free rate plus beta times the market risk premium. The market risk premium is 8% - 3% = 5%, so the expected return is 3% + 1.2(5%) = 9.0%. Beta measures the stock's sensitivity to market risk.

Question 13Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

In a simple linear regression of y on x, the estimated slope coefficient represents:

  1. change in predicted y per one-unit rise in x Correct answer.
  2. proportion of variation in y explained by x
  3. correlation between x and y
  4. predicted value of y when x equals zero

Explanation

The slope coefficient measures the estimated change in the fitted value of y for a one-unit increase in x. The intercept gives the predicted y when x equals zero. R-squared measures the proportion of variation explained, and correlation is a separate standardized measure.

Question 14Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

If market interest rates rise, the price of an existing fixed-coupon bond will generally:

  1. rise if the bond is held until maturity
  2. rise because coupon payments become more valuable
  3. fall since fixed cash flows are discounted more heavily Correct answer.
  4. remain unchanged because the coupon rate is fixed until maturity

Explanation

A bond's price is the present value of its fixed coupon and principal cash flows. Higher market interest rates raise the discount rate applied to those cash flows, lowering the present value. Bond prices and market yields therefore move inversely.

Question 15Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

A random sample of 64 observations is drawn from a population with mean 50 and standard deviation 16. Using the central limit theorem, the approximate probability that the sample mean exceeds 53 is closest to:

  1. 0.0228
  2. 0.1587
  3. 0.0668 Correct answer.
  4. 0.0401

Explanation

The standard error of the sample mean is 16 divided by the square root of 64, which equals 2. The z-score is (53 - 50)/2 = 1.5. The upper-tail normal probability beyond 1.5 is approximately 0.0668.

Question 16Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

A monopolist faces demand P=100-Q and has constant marginal cost MC=20 with no fixed costs. The profit-maximizing quantity is:

  1. 60
  2. 80
  3. 40 Correct answer.
  4. 20

Explanation

Total revenue is (100-Q)Q = 100Q-Q^2, so marginal revenue is 100-2Q. Set MR=MC: 100-2Q=20, giving Q=40. At this quantity the monopolist charges P=60.

Question 17Validation by Educational Experience (VEE) – Mathematical Statistics, Economics, Accounting and Finance

A firm has 60% equity and 40% debt in its capital structure. The cost of equity is 12%, pre-tax cost of debt is 6%, and the tax rate is 25%. Its weighted average cost of capital is closest to:

  1. 9.0% Correct answer.
  2. 9.6%
  3. 10.8%
  4. 7.2%

Explanation

WACC equals the weighted average of the cost of equity and the after-tax cost of debt. The after-tax cost of debt is 6%(1-0.25)=4.5%, so WACC is 0.60(12%) + 0.40(4.5%) = 9.0%. The tax adjustment is used because interest expense is tax-deductible.

Question 18Probability (P) Exam

A fair six-sided die is rolled. Given that the result is at least 4, what is the probability that the result is even?

  1. 2/3 Correct answer.
  2. 1/6
  3. 1/3
  4. 1/2

Explanation

Conditioning restricts the sample space to the three equally likely rolls 4, 5, and 6, so the denominator is 3/6. Two of these outcomes, 4 and 6, are even, giving 2/6. The ratio is (2/6)/(3/6) = 2/3.

Question 19Probability (P) Exam

Claim amounts follow an exponential distribution with mean 500. What is the probability that a randomly selected claim exceeds 1000?

  1. 0.5000
  2. 0.3679
  3. 0.1353 Correct answer.
  4. 0.8647

Explanation

For an exponential variable with mean θ, the survival function is S(x) = e^(-x/θ). With θ = 500 and x = 1000, the exponent is -2. Hence the probability is e^(-2) ≈ 0.1353.

Question 20Probability (P) Exam

A random variable X has E[X] = 3 and Var(X) = 4. Determine E[X^2].

  1. 13 Correct answer.
  2. 7
  3. 25
  4. 12

Explanation

The variance identity gives Var(X) = E[X^2] - (E[X])^2, so E[X^2] = Var(X) + (E[X])^2. Substituting the given values yields 4 + 9 = 13.

Question 21Probability (P) Exam

The number of claims reported in a week follows a Poisson distribution with mean 2. What is the probability that exactly one claim is reported?

  1. 0.2707 Correct answer.
  2. 0.1353
  3. 0.4060
  4. 0.5940

Explanation

For a Poisson variable, P(N = k) = e^(-λ)λ^k/k!. With λ = 2 and k = 1 this equals 2e^(-2) ≈ 0.2707.

Question 22Probability (P) Exam

An insurer wishes to choose 3 distinct policies from a group of 8 for an audit. How many different audit groups of 3 can be formed?

  1. 512
  2. 336
  3. 56 Correct answer.
  4. 24

Explanation

Choosing a group of 3 without regard to order is a combination: C(8,3) = 8!/(3!5!) = 56. Each unordered subset is counted once.

Question 23Probability (P) Exam

Thirty percent of policyholders are classified as high risk, and each high-risk policyholder files a claim during the year with probability 0.40. The remaining seventy percent are low risk, each filing a claim with probability 0.10. A randomly selected policyholder files a claim this year. What is the probability that this policyholder is high risk?

  1. 0.3684
  2. 0.3000
  3. 0.6316 Correct answer.
  4. 0.1200

Explanation

By Bayes' theorem the posterior weight is proportional to prior times likelihood. High risk contributes 0.30(0.40) = 0.12 and low risk contributes 0.70(0.10) = 0.07, so the total claim probability is 0.19. Dividing 0.12 by 0.19 yields 0.6316.

Question 24Probability (P) Exam

Given a random parameter Λ, the claim count N is conditionally Poisson with mean Λ. The parameter Λ has mean 2 and variance 1. Determine Var(N).

  1. 5
  2. 2
  3. 1
  4. 3 Correct answer.

Explanation

The conditional variance identity states Var(N) = E[Var(N|Λ)] + Var(E[N|Λ]). For a Poisson conditional distribution both terms equal Λ, so the variance simplifies to E[Λ] + Var(Λ) = 2 + 1 = 3.

Question 25Probability (P) Exam

Random variables X and Y have Var(X) = 4, Var(Y) = 9, and Cov(X,Y) = 3. Determine Var(2X - Y).

  1. 37
  2. 25
  3. 13 Correct answer.
  4. 19

Explanation

For constants a and b, Var(aX + bY) = a^2Var(X) + b^2Var(Y) + 2abCov(X,Y). Using a = 2 and b = -1 gives 4(4) + 9 - 2(2)(3) = 16 + 9 - 12 = 13.

Question 26Probability (P) Exam

Losses follow a normal distribution with mean 100 and variance 225. What is the probability that a loss exceeds 130?

  1. 0.0228 Correct answer.
  2. 0.0456
  3. 0.1587
  4. 0.9772

Explanation

Standardizing gives z = (130 - 100)/15 = 2. The requested probability is the upper tail 1 - Φ(2). From standard normal tables this is approximately 0.0228.

Question 27Probability (P) Exam

A loss X is uniformly distributed on the interval from 0 to 1000. An insurance policy pays max(0, X - 200). Calculate the expected payment under this policy.

  1. 320 Correct answer.
  2. 300
  3. 400
  4. 200

Explanation

The expected payment is the integral of (x - 200) times the density 1/1000 over the region where the loss exceeds the deductible. This gives (1/1000) times the integral from 200 to 1000 of (x - 200) dx, which equals 800^2/(2·1000) = 320.

Question 28Probability (P) Exam

Claims arrive independently on successive days, and each day has probability 0.3 of producing a claim. What is the probability that the third claim arrives on the fifth day?

  1. 0.1323
  2. 0.0567
  3. 0.0132
  4. 0.0794 Correct answer.

Explanation

The arrival time of the third success follows a negative binomial distribution with P(T = t) = C(t-1, 2)p^3(1-p)^(t-3). With t = 5 and p = 0.3 this equals 6(0.027)(0.49) ≈ 0.0794.

Question 29Probability (P) Exam

The moment generating function of X is M(t) = (0.2 + 0.8e^t)^3. Determine Var(X).

  1. 0.48 Correct answer.
  2. 2.40
  3. 0.80
  4. 0.60

Explanation

The moment generating function has the binomial form (1 - p + pe^t)^n with n = 3 and p = 0.8, so X is binomial with those parameters. Therefore Var(X) = np(1 - p) = 3(0.8)(0.2) = 0.48.

Question 30Probability (P) Exam

Three independent sources of claims each produce a first claim after a waiting time that is exponential with mean 100 days. Calculate the expected waiting time until the earliest of these first claims occurs.

  1. 25.00
  2. 100.00
  3. 300.00
  4. 33.33 Correct answer.

Explanation

The minimum of n independent exponential variables with common mean θ is itself exponential with mean θ/n. With θ = 100 and n = 3 the expected minimum is 100/3 ≈ 33.33.

Question 31Probability (P) Exam

Individual claim amounts are independent with mean 50 and standard deviation 40. A portfolio contains 64 such claims, and the normal approximation is used for the aggregate S. Estimate P(S > 3680).

  1. 0.0228
  2. 0.1587
  3. 0.0668 Correct answer.
  4. 0.9332

Explanation

The aggregate has mean 64(50) = 3200 and standard deviation 40 times the square root of 64, which is 320. Standardizing gives z = (3680 - 3200)/320 = 1.5, and the upper tail probability is 1 - Φ(1.5) ≈ 0.0668.

Question 32Probability (P) Exam

A loss variable X has probability density f(x) = (3/8)x^2 for 0 < x < 2 and zero elsewhere. Calculate E[X | X > 1].

  1. 1.8750
  2. 1.4063
  3. 1.6071 Correct answer.
  4. 1.5000

Explanation

The conditioning event has probability equal to the integral of (3/8)x^2 from 1 to 2, which is 7/8. The partial moment over the same region is the integral of x(3/8)x^2, equal to 45/32. Dividing gives (45/32)/(7/8) = 45/28 ≈ 1.6071.

Question 33Probability (P) Exam

Random variables X and Y are jointly normal with Var(X) = 9, Var(Y) = 4, and Corr(X,Y) = 0.5. Determine Var(Y | X = 12).

  1. 2.00
  2. 1.00
  3. 3.00 Correct answer.
  4. 4.00

Explanation

For a bivariate normal pair the conditional variance is Var(Y|X) = σ_Y^2(1 - ρ^2), which does not depend on the value of X. Substituting σ_Y^2 = 4 and ρ^2 = 0.25 gives 4(0.75) = 3.

Question 34Probability (P) Exam

The number of claims N on a portfolio is Poisson with mean 3. Individual claim amounts are independent of N, with mean 1000 and standard deviation 500. Determine Var(S), where S is the total claim amount.

  1. 4,500,000
  2. 750,000
  3. 3,750,000 Correct answer.
  4. 3,000,000

Explanation

The conditional variance identity gives Var(S) = E[N]Var(X) + Var(N)(E[X])^2 for a compound Poisson aggregate. Substituting 3(250,000) + 3(1,000,000) yields 750,000 + 3,000,000 = 3,750,000.

Question 35Financial Mathematics (FM) Exam

An account credits interest at a nominal annual rate of 8% convertible quarterly. Which effective annual rate does the account earn?

  1. 8.000%
  2. 8.160%
  3. 8.300%
  4. 8.243% Correct answer.

Explanation

The rate applied each quarter is 0.08/4 = 0.02, and over four quarters the accumulation factor is (1.02)^4 = 1.08243. The effective annual rate is therefore 0.08243, or 8.243%.

Question 36Financial Mathematics (FM) Exam

A payment of 5,000 is due in exactly 4 years. At an effective annual interest rate of 6%, what is its present value today?

  1. 3,903.74
  2. 4,032.26
  3. 6,312.38
  4. 3,960.47 Correct answer.

Explanation

The present value is obtained by discounting with the effective rate for four years: 5,000(1.06)^-4 = 5,000/1.262477 = 3,960.47.

Question 37Financial Mathematics (FM) Exam

A perpetuity-immediate pays 100 at the end of every year forever. At an effective annual interest rate of 5%, what is the present value of this perpetuity?

  1. 1,904.76 Correct answer.
  2. 2,000
  3. 2,100
  4. 1,500

Explanation

For a level perpetuity-immediate the present value equals the payment divided by the interest rate: 100/0.05 = 2,000.

Question 38Financial Mathematics (FM) Exam

Which of the following best describes a bond's coupon rate?

  1. The annual coupon payment divided by the bond's current market price
  2. The rate at which the bond's redemption value is assumed to accrue between coupon dates
  3. The annual coupon payment divided by the bond's face amount Correct answer.
  4. The rate of return earned by an investor who buys the bond and holds it to maturity

Explanation

The coupon rate is defined relative to the face (par) amount, so it equals the annual coupon payment divided by that face amount. Dividing the coupon by the market price instead gives the current yield.

Question 39Financial Mathematics (FM) Exam

An annuity-due pays 500 at the beginning of each year for 10 years. At an effective annual rate of 4%, what is the present value of these payments?

  1. 4,055.45
  2. 4,000.00
  3. 4,217.67 Correct answer.
  4. 4,386.37

Explanation

The annuity-due factor equals the annuity-immediate factor multiplied by (1 + i). Here a-angle-10 at 4% is 8.11090, so the due factor is 8.43533 and the present value is 500(8.43533) = 4,217.67.

Question 40Financial Mathematics (FM) Exam

A loan of 10,000 is repaid with a single payment at the end of 2 years, with interest at an effective annual rate of 7%. How much total interest is paid?

  1. 1,400.00
  2. 1,500.00
  3. 1,449.00 Correct answer.
  4. 1,490.00

Explanation

The accumulated repayment is 10,000(1.07)^2 = 11,449, so the interest component is 11,449 - 10,000 = 1,449. Interest in the second year itself earns interest, which is why the total exceeds two years of simple interest.

Question 41Financial Mathematics (FM) Exam

A loan of 20,000 carries interest at 6% effective, paid annually as it comes due. The principal is repaid by equal annual deposits into a sinking fund earning 4% effective, with the fund balance reaching 20,000 at the end of 5 years. What is the total annual outlay?

  1. 3,200.00
  2. 3,692.54
  3. 4,892.54 Correct answer.
  4. 4,747.94

Explanation

The annual loan interest is 20,000(0.06) = 1,200. The sinking fund deposit is 20,000/s-angle-5 at 4% = 20,000/5.41632 = 3,692.54, so the total outlay is 1,200 + 3,692.54 = 4,892.54.

Question 42Financial Mathematics (FM) Exam

A 10-year bond with face amount 1,000 pays annual coupons of 6% and is priced to yield 5% effective. What is the bond's price?

  1. 1,000.00
  2. 1,463.30
  3. 1,162.21
  4. 1,077.22 Correct answer.

Explanation

The price is the present value of the coupons plus the present value of the redemption amount: 60 a-angle-10 at 5% + 1,000 v^10 = 60(7.72173) + 1,000(0.613913) = 1,077.22.

Question 43Financial Mathematics (FM) Exam

A 2-year bond with face amount 1,000 pays annual coupons at 5% and is priced at a yield of 5% effective. What is its Macaulay duration?

  1. 2.000
  2. 1.859
  3. 1.905
  4. 1.952 Correct answer.

Explanation

The cash flows are 50 at time 1 and 1,050 at time 2, with present values 47.619 and 952.381 summing to 1,000. Macaulay duration is the present-value-weighted average time, (1(47.619) + 2(952.381))/1,000 = 1.952.

Question 44Financial Mathematics (FM) Exam

An investment of 10,000 returns 4,000 at the end of year 1 and 7,000 at the end of year 2. What annual effective yield does this investment earn?

  1. 5.80%
  2. 6.02% Correct answer.
  3. 7.00%
  4. 6.25%

Explanation

Set the equation of value 10,000 = 4,000v + 7,000v^2 and solve for v, giving v = 0.94319. Then 1 + i = 1/0.94319 = 1.06023, so the yield is about 6.02%.

Question 45Financial Mathematics (FM) Exam

An annuity-immediate pays 1,000 at the end of each year for 10 years, and every payment is reinvested at 5% effective until the end of year 10. What is the accumulated value at the end of year 10?

  1. 16,288.95
  2. 10,000.00
  3. 13,206.79
  4. 12,577.89 Correct answer.

Explanation

The payment made at time k accumulates for 10 - k years, so the total is 1,000 s-angle-10 at 5% = 1,000[(1.05^10 - 1)/0.05] = 12,577.89.

Question 46Financial Mathematics (FM) Exam

A nominal annual rate of 6% convertible monthly is equivalent to which nominal annual rate convertible semiannually?

  1. 6.075% Correct answer.
  2. 6.000%
  3. 6.168%
  4. 6.120%

Explanation

The monthly rate is 0.5%, so the annual accumulation factor is (1.005)^12 = 1.061678. Setting (1 + j/2)^2 equal to this factor gives 1 + j/2 = 1.030377, hence j = 6.075%.

Question 47Financial Mathematics (FM) Exam

A loan of 50,000 at 5% effective is amortized with 10 equal annual payments made at the end of each year. What is the outstanding balance immediately after the 5th payment?

  1. 32,866.33
  2. 25,000.00
  3. 21,965.64
  4. 28,034.36 Correct answer.

Explanation

The payment is 50,000/a-angle-10 at 5% = 50,000/7.72173 = 6,475.23. The prospective outstanding balance after the 5th payment equals the present value of the 5 remaining payments: 6,475.23 a-angle-5 at 5% = 28,034.36.

Question 48Financial Mathematics (FM) Exam

A 2-year bond with face amount 1,000 and annual coupons at 8% is priced at par. The 1-year spot rate is 5%. What is the 1-year forward rate for the second year implied by these prices?

  1. 8.00%
  2. 11.34% Correct answer.
  3. 11.09%
  4. 5.00%

Explanation

Pricing at par gives 1,000 = 80(1.05)^-1 + 1,080[(1.05)(1+f)]^-1, so 1.05(1+f) = 1,080/923.8095 = 1.16907 and f = 11.34%. The forward rate exceeds the par yield because the first-year spot rate is below 8%.

Question 49Financial Mathematics (FM) Exam

A liability of 1,000,000 is due in 5 years. A portfolio is immunized using only 3-year zero-coupon bonds and 10-year zero-coupon bonds, with all cash flows valued at a flat 5% effective rate. What fraction of the portfolio's present value should be placed in the 3-year bonds so that the Macaulay durations match?

  1. 62.50%
  2. 28.57%
  3. 71.43% Correct answer.
  4. 50.00%

Explanation

Duration matching sets 3w + 10(1 - w) = 5, where w is the weight in the 3-year bond. Solving gives 10 - 7w = 5, so w = 5/7 = 71.43%.

Question 50Financial Mathematics (FM) Exam

A stock currently trades at 50. A 1-year European call on the stock with strike 50 costs 6, and the 1-year effective risk-free rate is 5%. Assuming no dividends, what is the no-arbitrage price of the corresponding 1-year European put with strike 50?

  1. 2.38
  2. 6.00
  3. 3.62 Correct answer.
  4. 8.38

Explanation

Put-call parity states C - P = S - K(1 + r)^-1, so P = C - S + K(1.05)^-1 = 6 - 50 + 47.619 = 3.62.