QUANT METHODS MODULE 2

Question 1

2.1 recap: what are the FV and PV formulas (in relation to each other)

Answer 1

Question 2

2.1 What is a pure discount debt instrument?

Answer 2

A zero coupon bond. The investor pays less than the face value to buy the instrument and receives the face value at maturity.

The price that the investor pays depends on the instrument’s yield to maturity (the discount rate applied to the face value) and the time until maturity.

The amount of interest the investor earns is the difference between the fave value and the purchase price.

Question 3

2.1 How would you calculate with a negative yield?

Answer 3

Do the same just put the yield as a negative to 1 in the denominator and expect a purchase price higher than the face value

Question 4

2.1 What is a coupon rate? And what is the difference between it, and the YTM?

Answer 4

Is a percentage of the face value and determines the amount of the interest payments.

For example, a 3% annual coupon, $1000 bond pays 3% of $1000, or $30, each year.

The coupon rate and the yield to maturity are two different things. We only use the coupon rate to determine the coupon payment (PMT). The yield to maturity (I/Y) is the discount rate implied by the bond’s price.

Question 5

2.1 How would you calculate the price of an annual coupon bond?

Answer 5

Do the calculator solution in the exam - but good to know how to do it

Question 6

2.1 What are perpetual bonds or perpetuities? How can you calculate it’s PV?

Answer 6

Bonds that have no maturity date. It’s PV simplifies mathematically to the following:

Question 7

2.1 What is an amortising bond?

Answer 7

Is one that pays a level amount each period, including its maturity period. The difference between an amortizing bond and a fixed-coupon bond is that for an amortizing bond, each payment includes some portion of the principal. With a fixed-coupon bond, the enter principal is paid to the investor on the maturity date.

They are an example of an annuity instrument.

Question 8

2.1 How is the payment of an annuity calculated each period?

Answer 8

Question 9

2.1 What is the key differences between fixed income securities and equity securities?

Answer 9

Equity securities do not mature, and their cash flows may change over time.

Question 10

2.1 What is preferred stock?

Answer 10

Preferred stock pays a fixed dividend that is stated as a percentage of its par value (similar to the face value of a bond).

Question 11

2.1 What is the formula to calculate preferred stock value?

Answer 11

Because we can consider a preferred stock’s fixed stream of dividends to be infinite, we can use the perpetuity formula to determine its value:

Question 12

2.1 What is Common stock?

Answer 12

Common stock is a residual claim to a company’s assets after it satisfies all other claims. Common stock typically does not promise a fixed dividend payment. Instead, the company’s management decides whether and when to pay common dividends.

Question 13

2.1 What is a Discount Dividend Model and what are the three ways in which they can be used?

Answer 13

1. Assume a constant future dividend.
2. Assume a constant growth rate of dividends.
3. Assume a changing growth rate of dividends.

Question 14

2.1 In a DDM assuming a constant future dividend, how can we value an equity security?

Answer 14

Under this assumption, we can value a common stock the same way we value a preferred stock, using the perpetuity formula.

Question 15

2.1 In a DDM assuming a constant growth rate of dividends, how can we value the equity security?

Answer 15

With this assumption, we can apply the constant growth DDM, also known as the Gordon growth model. In this model, we state the value of a common share as follows:

Question 16

2.1 If a preferred stock share pays a constant dividend of $0.50 per share in perpetuity, how do we calculate its share price if investors demand a return of 8%? (just show formula)

Answer 16

Question 17

2.1 How can we rearrange the GGM for r and g?

Answer 17

Question 18

2.1 What should you recommend an investor to do “a course of action” if the fair PE value that you calculate for a stock is lower than the forward pe ratio?

Answer 18

Question 19

2.1 How to calculate PE ratio

Answer 19

Divide both sides by Earnings (so the numerator of GGM) D1/E1.

This will give the fair P/E ratio, so check this against listed P/E ratio.

Question 20

2.1 assuming a changing growth rate of dividends, how can we value an equity security?

Answer 20

This can be done in many ways. The example we will use here (and the one that is required for the Level I CFA exam) is known as a multistage DDM. Essentially, we assume a pattern of dividends in the short term, such as a period of high growth, followed by a constant growth rate of dividends in the long term.

Question 21

2.1 When can we use the gordon’s growth model?

Answer 21

When we are dealing with infinity

Question 22

2.2 Describe the relationship between prices and yields

Answer 22

Inverse

Question 23

2.2 Rearranging the constant growth DDM can show us:

Answer 23

the required rate of return on equity, and the implied growth rate

Question 24

2.2 What is the cash flow additivity principle?

Answer 24

The cash flow additivity principle refers to the fact that the PV of any stream of cash flows equals the sum of the PVs of the cash flows. If we have two series of cash flows, the sum of the PVs of the two series is the same as the PVs of the two series taken together, adding cash flows that will be paid at the same point in time. We can also divide up a series of cash flows any way we like, and the PV of the “pieces” will equal the PV of the original series.

Question 25

2.2 What is a 'replication'?

Answer 25

Using the principle of cash flow additivity to merge two cash flow to create a PV for the overall investment (or cash flows).

Question 26

2.2 What is the no-arbitrage principle?

Answer 26

otherwise known as the 'law of one price'. which says that if two sets of future cash flows are identical under all conditions, they will have the same price today (or if they don't, investors will quickly buy the lower-priced one and sell the higher-priced one, which will drive their prices together).

Question 27

2.2 What are the three examples of valuation based on the no-arbitrage condition?

Answer 27

1. Forward interest rates 2. Forward exchange rates 3. Option pricing using a binomial model

Question 28

2.2 how does the cash flow additivity principle work for forward interest rates?

Answer 28

The way the cash flow additivity principle applies here is that, for example, borrowing for three years at the 3-year spot rate, or borrowing for one-year periods in three successive years, should have the same cost today. This relation is illustrated as follows: (1 + S3)3 = (1 + S1)(1 + 1y1y)(1 + 2y1y). In fact, any combination of spot and forward interest rates that cover the same time period should have the same cost. Using this idea, we can derive implied forward rates from spot rates that are observable in the fixed-income markets.

Question 29

2.2 how does the cash flow additivity principle work for forward currency exchange rates?

Answer 29

Like interest rates, exchange rates can be quoted as spot rates for currency exchanges to be made today, or as forward rates for currency exchanges to be made at a future date. The percentage difference between forward and spot exchange rates is approximately the difference between the two countries' interest rates. This is because there is an arbitrage trade with a riskless profit to be made when this relation does not hold. For spot and forward rates expressed as price currency/base currency, the no-arbitrage relation is as follows:

Question 30

2.2 Current USD/GBP exchange rate = 1.25 USD per GBP. Continuously compounded interest rates are 2% in USD and 2.5% in GBP. Calculate the no Arbitrage 1-year forward exchange rate. (just say how I should do this)

Answer 30

Basically just what it should be given the interest rates, expanding the money in a year's time.

Question 31

2.2 how does the cash flow additivity principle work for an Option pricing model?

Answer 31

hopefully understand this when I look over these