Math Flashcards
(16 cards)
Correlation coefficient = -0.79
What is Macaulay Duration?
Suppose a company has a 3-year UK bond with a par value of £100, paying a coupon of 10% per annum and with a YTM of 12%. What is the bond’s Macaulay duration?
The weighted average maturity of a bond’s cash flows, measuring the bond’s sensitivity to interest rate changes.
aka how long does it take to get back the bond price
Present Value of a Bond example
Consider a 30-year, £100 coupon bond with 10% annual coupons with 6% YTM
Formula
How does bond value change as interest rate varies YTM)?
Conclusion: As interest rate (YTM) rises, bond value falls and vice versa.
Example:
Assume that a bond with a par value of $1000 and will be mature within 3 years
The coupon rate is 11.25% per annum and the coupon is paid semi-annually
Assume the YTM quote is 0.17% , what is the price of this Bond?
$1,331.40 - Premium
How to measure the sensitivity of a bond’s price to yield? – Modified Duration
What is it?
Using our 3-year bond from the previous example:
D = 2.73; YTM = 0.12; K = 1
A bond’s duration also tells investors how much a bond’s price might change when interest rates change
i.e. how much risk they face from interest rate changes.
Example
- DBC plc plans to pay its first dividend of 140p in four years’ time, and analysts expect that the dividend will grow at 2% per year thereafter in perpetuity. What is the value of a share of DBC stock if the firm’s cost of equity capital is 9%? (to the nearest penny):”
Assumption: If a company exists for forever its terminal value disappears.
How do we value equity within one-year investment horizon? — A discussion on Cost of Equity Capital
For example: XYZ Plc is trading at £100 per share today and it is expected to trade at £110 one year from now. What are the expected return, dividend yield and capital gain (loss) if the dividend one year from now is expected to be £5.00?
Assume that dividends are as follows:
Div 0 = 10, div 1 = 12, div 2 = 15, div 3 = 20,
div 4 = 28
Worked Example: The Coffee Growers Problem
(picture)