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My own FM212 > Fixed income ( 3-4) > Flashcards

Fixed income ( 3-4) Flashcards

1
Q

Why are bonds fixed income securities?

A

they provide periodic income payments at predetermined fixed interest rates. Whereas stocks were the cash flows received in years are not known.

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2
Q

So what is the issuance of a bond?

A

A bond is a security issued by a borrower( cash inflow) and purchased by an investor( cash outflow)

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3
Q

What is par value of a bond?

A

Face value or Principal ( The nominal value of the bond that is repaid to the bondholder at maturity.)

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4
Q

What is a bond coupon?

A

The periodic payment of interest on a bond. Generally fixed (can have floating rate bonds).

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5
Q

How do you calculate the annual coupon of a bond?

A

par value X coupon rate

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6
Q

What is the Coupon rate?

A

The annual coupon payment expressed as a percentage of the bond’s par value.

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7
Q

What is the Maturity date of a bond?

A

The specified date on which the par value of the bond must be repaid.

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8
Q

What is a Zero coupon bond?

A

A bond that pays no annual interest (coupons) but is sold below par so all the compensation is paid to the zero coupon bondholder in the form of capital appreciation. ( if your not getting coupon you are not going to pay more than what you will get in FV)

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9
Q

What is a coupon bond?

A

A bond that pays regular coupon interest payments up to maturity, when the par value is also paid.

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10
Q

When is a bond said to be trading at a discount?

When is a bond said is said to be trading at a premium.?

A

A bond trading below it’s par value

A bond trading above it’s par value

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11
Q

A 5 year zero has a face value of £10,000 and is priced at £9750
Show this on a diagram

A
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12
Q

With the coupon bond, what does the investor get at the end of maturity and are coupon payments have an irregular payment structure?

A

On the maturity date, the bondholder receives both a coupon payment and
the par value.
At regular intervals until maturity the bondholder receives a coupon payment.
These payments could be made annually, semi-annually or quarterly.
These coupon payments are usually the same at every payment date.

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13
Q

A 2 year 6% coupon bond with annual coupons and a face value of £100.
Show on diagram

A
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14
Q

What is the Yield to maturity of a bond?

A

The YTM is the constant, hypothetical discount rate that, when used to compute the PV of a bond’s cash flows, gives you the bond’s market price as the answer.

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15
Q

What 4 things do you need to calculate YTM?

A

1) current price
2) Time left to maturity
3) par value
4) Annual interest payment

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16
Q

1) What does a high bond price mean?

2) What does a low bond price mean?

A

A higher bond price must mean a lower YTM

A lower bond price must mean a higher YTM

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17
Q

How would you calculate YTM here what does it mean if YTM =. coupon rate?

A

We know that it has to be less than 6%, as the bond price is higher than FV of 100, so YTM < Coupon rate.
When YTM = Coupon rate, it trades at par. ( 100

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18
Q

Assume that today is January 2018. A German Government bond (Bund) pays
a 5.375% annual coupon, every year for 6 years. The face value of the bond is
€100. Its YTM is 3.8%.
What is the market price of the bond? ( Just PV)

A
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19
Q

Why can prices and thus YTM’s very through a bonds lifetime?

A

Because of the term structure of interest rates. ( we will explain this later)

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20
Q

What is the relationship between bond prices and interest rates and why?

A

Bond prices are negatively related to interest rates.
If interest rates go up, cash flows are discounted more heavily, and the price (PV) goes down.
If interest rates go down, cash flows are discounted less heavily, and the price (PV) goes up.

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21
Q

Just to clarify how again how do we know if a coupon bond is trading above par or below par?
, in a world of positive interest rates, zero coupon bonds must
always be priced ?

A

1)If the coupon rate on a bond is greater than the YTM, then the price of the
bond will be above par (or face value).
If a bond’s coupon rate is below the YTM, then the bond’s price will be
below par.
2) below par

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22
Q

What is a common stock?

What is an IPO?
What is the secondary market?

A

1) Security representing a share in the ownership of a
corporation.
2) The first sale of stock in a corporation to the public.
3) A market, often a stock exchange in which previously issued shares are traded amongst investors.

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23
Q

What are dividends?

A

Payments made by companies to shareholders. These

are usually ex-ante uncertain (unlike bond coupons).

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24
Q

What is a dividend yield?

What is P/E ratio?

A

1) Ratio of annual dividend to share price.

2) Share price divided by earnings per share

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25
Q

1) What is the market value of a company?

2 What is the book value of a company?

A

1) The total stock market value of the firm’s stock (i.e. price per share multiplied by number of shares outstanding).
2) Accounting value of the firm’s equity as reflected on the company’s balance sheet.

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26
Q

What is the liquidation value of a firm?

A

The amount that would be available to shareholders if the firm was liquidated and all creditors paid off.

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27
Q

You buy a share today, defined as time t=0, in a corporation that has a current
price of P0. You know that at the end of one year, t=1, the firm will pay you a
dividend D1 and after the payment of the dividend you will be left with a share
worth P1. You don’t know with certainty the values of D1 and P1 today.
You wish to estimate the percentage one-year return you will obtain from
holding the stock
Give the formula for Measuring expected return to holding a share

A

Called be capital depreciation too.

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28
Q

We know the expected return of holding a share is.
We can rearrange this, assuming investors want a particular constant return
if investors require a return of E(r) and expect dividends of D1 and a future price
of P1 at t=1 then using PV techniques, what is the price today of holding the stock.
What is the expected price at E( P1)?

A
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29
Q

What would be expectation of price at E0(p2)?

A

It would be expectation of dividend at time 3 + price at time 3 then discount it one period to get time 2.

30
Q

So now in general what is the stock pricing equation ( DIVIDEND DISCOUNT MODEL, what is the dividend discount model?
)
What are some properties?
What is attached is for the second part?( explain|)

A

The dividend discount model is a method of valuing the stock of a company based on its future dividend payments. The model assumes that the intrinsic value of a stock is equal to the present value of all future expected dividend payments.

Just reiterating here that when dividends are not constant, make sure you discount well e.g. as you can see
what is attached is the price discounted by 2 time periods.
The price is basically the expectation of dividend discounted today.

31
Q

What is the stock price formula, for a stock that pays out constant dvidends starting one period after the point of valuation?

A

Same formula as perpeutiy

32
Q

What is the formula for Stock Prices when Dividends Grow at a Constant Rate and start one period after the point of valuation?
What is the formal name for this and what does this imply?

A

The gordon growth model

33
Q
A
34
Q

Where are dividends paid out of? If a firm chooses to invest more today and pays a lower dividend, what will happen to stock price?

A

1) Dividends must be paid out of a firm’s net earnings.
2) If a firm chooses to invest more today and pays a lower dividend, that might
raise stock prices ( invest in NPV projects as stock price is determined after dividends are paid. as it allows the firm to make greater dividend payments in
future.

35
Q

What is Payout ratio and Plowback ratio?

A

Payout = The ratio of dividends to earnings
Plowback ratio = is the proportion of earnings retained by the firm and used
for investment.

36
Q

What is ROE and whats the formula?

A

( basically how efficient the company is at making profit for shareholders)

37
Q

What is the formula for a firms earning growth rate? ( this tells us that the firms earnings can grow governed by its ROE and by its plowback ratio.

A
38
Q

If the payout ratio i.e. (1 – plowback ratio), and ROE are constant, what is the dividend growth rate?

A

If dividend payout ratio is the same, assuming the residual amounts after you pay for new investment is whats is left for dividends, this must mean the dividend growth rate = EGR.
Investing in Positive nPV projects meanings firms net earnings higher, so dividend higher.

39
Q

We are going to prove that with 2 firms, if one plowbacks its earnings,it will have a higher stock price.
Part 1) Firm 1 earns £8.33 per share every year and pays out all of this to investors. It’s required rate of return is 15%. What is its stock price?

A
40
Q

We are going to prove that with 2 firms, if one plowbacks its earnings,it will have a higher stock price.
Part 2) Firm 2 has an identical required return to Firm 1 and an identical earnings forecast for next year (i.e. £8.33). Instead of paying all of its earnings as dividends, it commits to plowing back 40% of them. It’s ROE is 25%. What is the stock price?

A

Given the assumption of constant ROE and plowback ratio the constant growth
rate in dividends is:
g ROE Plowback Ratio =0.25 0.4=0.1

41
Q

So what is the initution behind why firm 2 has a higher share price?

A

This is because its ROE is greater than the required return ( 0.25>0.1) so retaining earnings generates returns that are above the discount rate.
If the ROE was equal to the required return, the two firms would be worth
the same amount

42
Q

What is the Present Value of Growth Opportunities

(PVGO)?

A

The difference in value between the firm that plows back earnings and the
firm that does not
In this case this is equal to £100 - 44.44 = PVGO

43
Q

Using PVGO what is the price of share

A
44
Q

Why are E/P ratios not a good measure of required returns?

A

They will dramatically understate required returns for firms with large PVGO. Lesson, don’t use E/P ratios to estimate required returns unless you adjust for growth.

45
Q

If the expected return on new investment = the cost of capital, what happens to stock price?

A

NPV = 0 hence stock price is the same.

46
Q

So interest rates are the not the same for different maturites , with annuites we used flat rate for different time periods ( which were the same), whereas when cash flows are different, and is not an annuity or perpetuity, what do we use and define it ?

A

Spot rate = Bonds are priced using spot rates.If you’re pricing a stream of cash flows, each cash flow has its own relevant interest rate depending on when it arrives.

47
Q

We are assuming here that we are looking at government bonds, so no default risk, What rate is used to price government bonds?

A

The spot rate.

48
Q

What is Arbitrage ( 2 definitions)

A
  1. An investment strategy that has a positive cash flow today and zero cash
    flows in the future in all states of nature.
  2. An investment strategy that has zero cash flows today and strictly non
    negative cash flows in all states of nature in the future with at least one positive future cash flow in a future state of nature.
49
Q

What does this show?

A

Positive cash flow today for a zero cash flow in the future ( borrow PV of £110 and pay back with interest)

50
Q

Describe the process of short selling a bond?

A

Steps:
Date 0: Borrow the bond from a broker ( cash inflow) and sell the bond in the market.

Between dates 0 and 1: Compensate the broker for any coupons the bond pays.

Date 1: Buy the bond in the market ( when it falls in price) and return the bond to the broker.

A short sale is profitable if the bond price goes down.

51
Q
A

1) Find implied spot rates for the zero coupon bonds

52
Q

What ensures using the spot rates to determine the price of the coupon bond is actually the market price?

A

We can synthetically replicate Bond A using Bonds B and C.

53
Q

What does the law of one price state?

A

if you have 2 assets that have the same cash flows in the future, they must have the same price today. If they don’t have the same price today, there must be a aribtrage opportunity. ( shorting an asset( sell when high) and long(buy when low)

54
Q

What does it mean when a question asks you about a replicating portfolio?

A

It wants you to replicate the portfolio, which gives same price today.

55
Q

What is the replicating portfolio for the coupon bond A?

A

The replicating portfolio consists of being long (buying) 0.1 units of Bond B and
long (buying) 1.1 units of Bond C.
0.1(£90) + 1.1 ( £80) = £97.
So no aribitrage price of bond is £97

56
Q

Show this replicating portfolio on diagram
The replicating portfolio consists of being long (buying) 0.1 units of Bond B and
long (buying) 1.1 units of Bond C.
0.1(£90) + 1.1 ( £80) = £97.

A

Think about it like this, we are trying to match cashflows to bond A buying 1 unit of bond b at time =1 will get you 100, buying 2 = 200, you wont to match cash flow at time = 1 of bond A (10) - remember bond B.
For bond C we trying to match cash flows at t=2 for bond C, so i buy 1.1 units .

57
Q

If the price in the market is £98 for bond A, is there an arbitrage opportunity and what is the strategy? How much profit should we make?
HINT the 2 ASSETS ARE BOND A and replicating portfolio
BTW in reality do we short just one bond?

A

£1 profit
you want the larger number at time = 0 ( short) and you want to buy low ( long).
So you short bond A ( sell high), remember between time 0 and 2 you need to maintain the original owner coupon payments, and pay the coupon + par value at maturity.
Long ( buy low) Bond A £97, meaning you get the cash flows at time = 1 and 2.
No in reality we short much more than one bond.
Full arbitrage strategy = sell 1 unit of bond A, buy 0.1 units of bond B and buy 1.1 units of bond C.

58
Q

When interest rates rise, the price of any bond is going to fall. Then the question is, is there a metric we can use to evaluate a bond and see how sensitive its going to be given its change in interest rate?

A

The Macaulay Duration is simply a weighted average of the years in which the
bond pays its cash flows.

59
Q

What is the formula for macualay duration?

A
60
Q

Work out Maculay duration?

Compare what it means if another bond had a MacD of 7 years

A

PV of cash flow is just 40/(1+y)^t
PV of time waited cash flows its just the pV multiplied by the time period.
Makes sense that PV of cash flows is trading less than FV because Market rate of interest > coupon rate. ( people can get higher interest rate on market)

We then just do the sum present value of the time weighted cash flows / sum of present value cash flow.
4523.61/978.05 = 4.63 years .
The investor who gets the 7 years bond, will be exposed to more interest rate risk ( if there is a change in interest rate. e.g. interest rate sky rocket up, that affects price of bond with a higher duration )

61
Q

What is Modified duration?

Work this out

A

Dmod= Dmac/ (1+y)

where y/k k = compounding frequency ( so semi - annually = 2 quarterly = 4

62
Q

How do you measure the Sensitivity of Bond Prices to Interest Rates (Hint: use Modified Duration)

A
63
Q

Suppose the YTM of a three year 1.5% annual coupon government bond increases from 0.745% to 0.76%. The face value of the bond is £1000. Use the modified duration of the bond to estimate the new price of the bond

A
64
Q

Whats another way to explain the sensitivity in bond prices when interest rate changes ?

A

Lets look at price yield curve, if we take derartive of the curve, the Modified duration, is the derartive of the bonds price, with respect to the yield. So higher MOD means bond price more sensitive to changes in the yield.

65
Q

What is a forward rate?

A

The interest rate we could guarantee today for a loan or investment that occurs in the future. w

66
Q

We are being asked about the one year spot rate in one years time.
1f1 has to be a specific number or we can make aribtrage.
At time 0 the forward rate is agreed.
First of all what are the 2 strategies here saying?

A

1) Just invest over 2 years and directly earn the 2 year spot rate
2) or take money today and invest in one year spot rate and simultaneously at time 0, agree the rate you are going to earn at time 1 to 2

67
Q

What if the forward rate is less than 0.75 too?

A
68
Q

What is a term structure of interest rates ?

A

it is a mapping between maturities and spot rates at those maturites,.
On a graph the plot is spot rates on y axis and on x axis maturity.

69
Q

What are 2 types of yield curve?

A
70
Q

What are the 3 theories to explain the term structure of interest rates?

A

Unbiased expectations theory
Liquidity premium theory
Market segmentation Hyphothesis.

71
Q

How to work out book equity per share?

A

Book equity per share in previous years + EPS(1-payout)

My own FM212 (13 decks)

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