cyber21

In addition to the usual parameters that describe a normal distribution, to completely describe 10 random variables, a multivariate normal distribution requires knowing the:

A) overall correlation.

B) 10 correlations.

C) 45 correlations.

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The number of correlations in a multivariate normal distribution of n variables is computed by the formula ((n) × (n-1)) / 2, in this case (10 × 9) / 2 = 45.

cyber21

A multivariate distribution:

A) specifies the probabilities associated with groups of random variables.

B) applies only to binomial distributions.

C) gives multiple probabilities for the same outcome.

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This is the definition of a multivariate distribution.

cyber21

In which of the following cases would Monte Carlo simulation least likely be needed? Payoff of a:

A) GNME.

B) roulette wheel.

C) European option.

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The probability distribution of a roulette wheel would be easy to estimate using empirical or a priori methodology.

cyber21

Monte Carlo simulation is necessary to:

A) reduce sampling error.

B) compute continuously compounded returns.

C) approximate solutions to complex problems.

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This is the purpose of this type of simulation. The point is to construct distributions using complex combinations of hypothesized parameters.

cyber21

Mei Tekei just celebrated her 22nd birthday. When she is 27, she will receive a $100,000 inheritance. Tekei needs funds for the down payment on a co-op in Manhattan and has found a bank that will give her the present value of her inheritance amount, assuming an 8.0% stated annual interest rate with continuous compounding. Will the proceeds from the bank be sufficient to cover her down payment of $65,000?

A) Yes, Tekei will receive $68,058.

B) Yes, Tekei will receive $67,028.

C) No, Tekei will only receive $61,878.

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Because the rate is 8% compounded continuously, the effective annual rate is e0.08 - 1 = 8.33%. To find the present value of the inheritance, enter N=5, I/Y=8.33, PMT=0, FV=100,000 CPT PV = 67,028.

Alternatively, 100,000e-0.08(5) = 67,032.

cyber21

The continuously compounded rate of return that will generate a one-year holding period return of -6.5% is closest to:

A) -6.7%.

B) -6.3%.

C) -5.7%.

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Continuously compounded rate of return = ln(1 − 0.065) = -6.72%.

cyber21

Given a holding period return of R, the continuously compounded rate of return is:

A) ln(1 + R).

B) eR − 1.

C) ln(1 − R) − 1.

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This is the formula for the continuously compounded rate of return.

cyber21

If a stock decreases from $90 to $80, the continuously compounded rate of return for the period is:

A) -0.1250.

B) -0.1178.

C) -0.1000.

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This is given by the natural logarithm of the new price divided by the old price; ln(80 / 90) = -0.1178.

cyber21

Assume an investor purchases a stock for $50. One year later, the stock is worth $60. After one more year, the stock price has fallen to the original price of $50. Calculate the continuously compounded return for year 1 and year 2.

Year 1

Year 2

A) 18.23% -18.23%

B) 18.23% 16.67%

C) -18.23% -18.23%

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Given a holding period return of R, the continuously compounded rate of return is: ln(1 + R) = ln(Price1/Price0). Here, if the stock price increases to $60, r = ln(60/50) = 0.18232, or 18.23%.
Note: Calculator keystrokes are as follows. First, obtain the result of 60/50, or 1. On the TI BA II Plus, enter 1.20 and then click on LN. On the HP12C, 1.2 [ENTER] g [LN] (the LN appears in blue on the %T key).The return for year 2 is ln(50/60), or ln(0.833) = negative 18.23%.

cyber21

If a stock decreases in one period and then increases by an equal dollar amount in the next period, will the respective arithmetic average of the continuously compounded and holding period rates of return be positive, negative, or zero?

A) Zero; zero.

B) Positive; zero.

C) Zero; positive.

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The holding period return will have an upward bias that will give a positive average. For example, a fall from 100 to 90 is 10%, and the rise from 90 to 100 is an increase of 11.1%. The continuously compounded return will have an arithmetic average of zero. Since we can sum continuously compounded rates for multiple periods, the continuously compounded rate for the two periods (0%), means the rates for the two periods must sum to zero, and their average must therefore be zero.