Math Flashcards

(16 cards)

1
Q

Correlation coefficient = -0.79

A
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2
Q
A
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3
Q

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?

A

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

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4
Q

Present Value of a Bond example

Consider a 30-year, £100 coupon bond with 10% annual coupons with 6% YTM

Formula

A
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5
Q

How does bond value change as interest rate varies YTM)?

A

Conclusion: As interest rate (YTM) rises, bond value falls and vice versa.

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6
Q

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?

A

$1,331.40 - Premium

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7
Q

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

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.

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8
Q

Example

  1. 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):”
A

Assumption: If a company exists for forever its terminal value disappears.

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9
Q
A
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10
Q

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?

A
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11
Q
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12
Q

Assume that dividends are as follows:

Div 0 = 10, div 1 = 12, div 2 = 15, div 3 = 20,
div 4 = 28

A
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13
Q
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14
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15
Q
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16
Q

Worked Example: The Coffee Growers Problem
(picture)