Module 9.3: Lognormal Distribution, Simulations

Question 1

What is Roy’s safety-first criterion?

Answer 1

States that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level “the threshold level”

Question 2

What is the formula for Roy’s safety-first criterion?

Answer 2

E(Rp)-RL / standard deviation of p (RL = threshold level - typically 0)

Question 3

What are the two steps of the safety-first criterion?

Answer 3

1) Calculate the SFratio (formula)

2) choose the portfolio that has the largest SFRatio.

Question 4

What is a lognormal distribution?

Answer 4

Lognormal distribution is generated by the function e^x, where x is normally distributed, thus the name.

Question 5

What are the main differences between a normal and lognormal distribution?

Answer 5

1) Lognormal distribution is skewed to the right
2) Lognormal distribution is bounded by zero so that it is useful for modeling asset prices which never take negative values.

Question 6

What are discretely compounded returns?

Answer 6

Simply the compound returns we are familiar with, given some discrete coumpounding period, such as semi annual or quarterly.

Question 7

How can you calculate the continuous compounding rate?

Answer 7

effective annual rate = e ^R - 1

or ln (current price / purchase price)

or ln (1 + return)

Question 8

What is Monte Carlo simulation?

Answer 8

A technique based on the repeated generation of one or more risk factors that affect a security value, in order to generate a distribution of security values.

Question 9

What is Monte Carlo simulation used for?

Answer 9

1) Valuing complex securities
2) Simulate the profits / losses from a trading strategy
3) Calculate estimates of value at risk
4) Simulate pension fund assets & liabilities over time
5) Value portfolios of assets that have nonnormal returns

Question 10

What are the limitations of Monte Carlo simulation?

Answer 10

fairly complex and will provide answers that are no better than the assumptions about the distributions of the risk factors.

Question 11

What is historical simulation?

Answer 11

Based on actual changes in value or actual changes in risk factors over some prior period. Advantages is grounded in reality, but the past is not an accurate predictor of the future.