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Financial and Capital Markets > Financial & Capital Markets > Flashcards

Financial & Capital Markets Flashcards

1
Q

Time Value of Money

A

the difference in money today and at a future time

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2
Q

Net Present Value

A

PV(Benefits)-PV(Costs)

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3
Q

Risk Free Interest rate (rf)

A

The interest rate at which money can be borrowed or lent without risk over that period

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4
Q

Interest rate factor

A

(1+rf) - the exchange rate across time

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5
Q

Discount factor

A

1/1+r

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6
Q

Positive NPV

A

means it is probably best to take up the project

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7
Q

NPV Decision rule

A

When making an investment decision, take the alternative with the highest NPV.Choosing this alternative is equivalent to receiving its NPV today.
If it down to a choice between projects we should always aim to chose the project with the highest NPV

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8
Q

Arbitrage

A

The practice of buying and selling equivalent a goods in different markets of take advantage of a price difference

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9
Q

Arbitrage opportunity

A

making a profit without taking any risk or making any investment

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10
Q

normal market

A

A competitive market where no arbitrage opportunities exist.

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11
Q

Law of One Price

A

If equivalent investment opportunities trade in different competitive markets, then they must trade for the same price in both markets.

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12
Q

financial security (security)

A

An investment opportunity that trades in a financial market

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13
Q

A bond

A

A security sold by governments and corporations to raise money from investors today with the promise of payment in the future.

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14
Q

No arbitrage price of a security

A

=PV(All cash flows paid by the security)

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15
Q

Return

A

Percentage gain you earn from investing in a bond.

Gain at the end of the year/Initial Cost

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16
Q

Portfolio

A

Combination of securities

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17
Q

Risk Aversion

A

preference to safe investments rather than those that carry risk

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18
Q

risk premium

A

is the difference between the expected return on an investment - the risk free interest rate of the investment

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19
Q

Compounding

A

The process of moving a value of money from one point in time to another.

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20
Q

Compound interest

A

“Earning interest on interest”.

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21
Q

Discounting

A

Finding the equivalent value today of a future cash flow

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22
Q

Perpetuity

A

Stream of Cash Flows that occur at regular intervals and last forever.

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23
Q

in arrreas

A

When the first payment of a perpetuity occurs at the end of the first period.

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24
Q

Present Value of a Perpetuity

A

C/r

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25
Q

Annuity

A

Stream of N cash flows paid at regular intervals

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26
Q

Present Value of an annuity

A

PV(annuity of C for N periods with interest rate r=

C/r(1-1/(1+r)^N)

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27
Q

Future Value of an Annuity

A

PV x (1+r)^N

C x 1/r((1+r)^N - 1)

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28
Q

Growing Perpetuity

A

Stream of cash flows that occur at regular intervals and grow at a constant rate forever.

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29
Q

Present Value of a growing perpetuity

A

= C/r-g where r is the interest rate and g is the amount we withdraw each year.

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30
Q

Internal Rate of Return

A

The interest rate that sets the NPV of cash flows to zero

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31
Q

Growing annuity

A

a cash flow that grows at a constant rate g. The cash flow stops after a finite number of years

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32
Q

Present value of a growing annuity

A

PV = c/r-g * (1 - (1+g)^N/(1+r)^N)

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33
Q

Effective Annual Rate (EAR)

A

The total amount of interest that will be earned at the end of the year. It considers the effect of compounding

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34
Q

Annual Percentage Rate (APR)

A

Simple interest without the effect of compounding. It is typically less than the EAR. It cannot be used as a discount rate and thus must be converted to an EAR

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35
Q

APR —> EAR formula

A

1+EAR = (1+APR/k)^k where k is the compounding periods

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36
Q

The fisher effect

A

Is the relation between the nominal interest rate, real interest rate and inflation. Given by 1+real = 1+nominal/1+inflation

An increase in interest rates will typically reduce the NPV of an investment

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37
Q

Term structure

A

The relationship between the investment term and the interest rate

Can be used to compute the present and future values of risk free investments over different investment horizons

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38
Q

A steep yield curve indicates…

A

that interest rates are expected to rise. It is common on short interest rates and inflation is low or an economy is emerging from a recession

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39
Q

An inverted yield curve indicates….

A

the interest rates are expected to decline in the future

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40
Q

A flat yield curve indicates…

A

occurs when interest rates are transitioning

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41
Q

A humped yield curve…

A

occurs when rates are transitioning or market participants are attracted to a particular maturity segment of the market

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42
Q

What risk do treasury securities hold?

A

None. They are risk free

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43
Q

After tax interest interest rate

A

the amount of interest an investor can keep once the earnings have been taxed.

r~ = r * (1- t) where t is the tax rate

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44
Q

Opportunity cost of capital

A

The best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted

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45
Q

What choice should be made when rules of investment conflict?

A

Follow the NPV

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46
Q

Internal rate of return investment rule?

A

Take any investment where the IRR exceeds the cost of capital and turn down an investment where it does not exceed the cost of capital

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47
Q

When will the IRR work?

A

for standalone projects when all negative cash flows precede the positive cash flows

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48
Q

What situations would the IRR conflict with the NPV

A

Delayed investments.
Non-existent IRR
Multiple IRR

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49
Q

What could the reason be for IRR not working for delayed investment?

A

The IRR may appear to be greater than the cost of capital however when the NPV is calculated the NPV could be negative indicating the investment should not be undertaken

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50
Q

What could be the issue with a non-existent IRR?

A

Here it would see there is no clear cut way of deciding on the project using the IRR rule but in this situation it could be that the NPV will always be positive (or negative)

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51
Q

What could be the issue with multiple IRRS?

A

Wouldn’t know when IRR to make and there is also bound and so it can make the decision difficult. To rectify this rely on the NPV

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52
Q

What is the advantage of the IRR?

A

It can measure the average return of the investment and the sensitivity of the NPV to any estimation error in the cost of capital

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53
Q

The Payback Rule

A

If the payback period is less than a prespecified time you accept the project .

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54
Q

Payback period

A

is the amount of time it take to recover or payback the initial investment

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55
Q

Disadvantages to the payback rule method

A

Ignores projects cost of capital and time value of money
Ignores cash flows after the payback period
Relies on ad hoc decision criterion about the cut off period
Project chosen based on this may not have a positive NPV

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56
Q

Advantages to the payback rule method

A

Easy to understand and apply
focuses on the liquidity of an investment project
commonly used when the capital investment is small and the horizon is short

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57
Q

The discounted payback period

A

Involves considering the time value of money by taking the discount rate into consideration. However, by the time you have calculated this you might as well work out the NPV

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58
Q

When using the IRR rule what must we take into consideration in order to avoid mistakes?

A

Projects differ in:
Scale of investment
timing of cash flows
riskiness

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59
Q

What effect does the scale have when comparing projects?

A

If a size doubles the NPV will double. However, the IRR does not

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60
Q

What effect does the timings of cash flow have when comparing projects?

A

The IRR can change as a result of differences in timings and so can change the rankings of the IRR. The NPV isnt affected

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61
Q

What effect does the risk have when comparing projects?

A

An IRR that is safe for a safe project need not be attractive for a riskier project

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62
Q

Incremental IRR rule

A

Apply the IRR rule to the difference between the cash flows of the mutually exclusive alternatives. It tells us the discount rate at which it becomes profitable to switch from one project to another

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63
Q

Shortcomings of the IRR

A

incremental irr may not exist
multiple irrs
The fact the the IRR exceeds the cost of capital does not mean the NPV is positive
when there are different costs of capital for projects it is not obvious which one to use.

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64
Q

Profitability index

A

The value created in terms of NPV for the amount of resource consumed. Starting with the highest ranking and move down the ranking until all the resource is consumed

NPV/resource consumed

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65
Q

Shortcomings of the profitability index

A

the set of projects taken following the profitability index ranking exhausts all available resources
with multiple resource constraints the index could break down completely

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66
Q

Bond certificate

A

states the terms of the bond

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67
Q

maturity date

A

the final repayment date

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68
Q

term

A

the time remaining until repayment date

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69
Q

Coupon

A

promised interest payments

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70
Q

Fave value

A

notional amount used to compute the interest payments

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71
Q

coupon rate

A

amount of each coupon payment (express as apr)

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72
Q

Coupon payment

A

CPN = coupon rate*facevalue/ no. of coupon payments per year

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73
Q

Yield to maturity

A

discount rate that sets the present value of the promised bond equal to the market price of the bond

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74
Q

Zero-coupon bond

A

a bond which does not make coupon payments

Always sells at a discount

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75
Q

Yield to maturity of a Zero-Coupon bond

A

P= facevalue/(1+YTM)^n

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76
Q

Law of one price guarantees what?

A

That the risk free interest rate equals the yield to maturity on a zero-coupon bond

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77
Q

Risk free interest rate with maturity n equals…

A

rn=YTMn

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78
Q

Zero coupon yield curve

A

a plot of the risk free zero coupon bonds as a function of the bonds maturity date

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79
Q

Coupon bonds

A

regular coupon interest payments and pays face value at maturity

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80
Q

Yield to maturity of a zero-coupon bond

A

P = CPN *1/y(1-1/1+y)^N) + facevalue/(1+y)^N

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81
Q

A bond is selling at a discount when…

A

its price is less than its face value and coupon rate is greater than YTM

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82
Q

A bond is selling at par when….

A

its price is equal to the face value and the coupon rate is equal to the YTM

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83
Q

A bond is selling at premium when…

A

its price is greater than the face value and the coupon rate is less than the yield to maturity

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84
Q

If a bond’s yield to maturity has not changed…

A

the IRR of an investment in the bond equals its yield to maturity even if you sell the bond early

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85
Q

Duration

A

measures the sensitivity of a bond’s price to change in the interest rate

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86
Q

As interest rates rise what happens to bond prices?

A

Bond prices fall

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87
Q

As interest rate fall what happens to bond prices?

A

Bond prices increase

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88
Q

Bond with high duration….

A

are more sensitive to changes in the interest rate

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89
Q

Price of a coupon bond

A

P=CPN/(1+ytm) +CPN/(1+ytm)^2……CPN+facevalue/(1+ytm)^N

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90
Q

Corporate bonds

A

bonds issued by corporations

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91
Q

credit risk

A

risk of default

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92
Q

yields of corporate bonds with high credit risk…

A

will be higher than they would be for identical default free bonds

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93
Q

Dividend discount model

A

potential cash flows…. Dividend + Sale of stock

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94
Q

Equity cost of capital…

A

the expected return of other investments available in the market rE

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95
Q

P0= Div1+P1/1+rE

A

Price of a stock today when using the equity cost of capital

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96
Q

If the actual stock price is found to be less than what is found to be true

A

there is a positive NPV

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97
Q

Solving for total return rE

A

Div1+P1/P0 which can be split into divided yield and capital gain rate

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98
Q

Dividend yield

A

the percentage return the investor expects to earn from the dividend paid

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99
Q

Capital gain rate

A

expresses the capital gain as a percentage return

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100
Q

Price of a Share for two years

A

P0 = Div1/1+rE + Div2+P2/(1+rE)^2

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101
Q

Total return of a stock

A

sum of dividend yield and capital gain rate

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102
Q

Dividend discount model

A

Initial price of a stock where the horizon N is arbitrary

P0 = Div1/1+rE + Div2/(1+rE)^2…+DivN/(1+rE)^N + PN/(1+rE)^N

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103
Q

What is the price of a stock if it is held forever?

A

Is equal to the present value of the expected future dividends it will pay

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104
Q

Constant dividend growth model

A

models dividends which grow at a constant rate

P0=Div1/rE-g where g is the growth rate

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105
Q

Total return of a growing dividend

A

rE=Div/p0 +g where g is capital gain

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106
Q

Implied return

A

Pn=P0(1+IR)^n

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107
Q

What is the dilemma faced when a company wants to increase its share price?

A

There has to be a trade off between paying out dividends and instigating growth. In order to facilitate growth some of the company earnings will have to go on investment rather than be paid out as dividends

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108
Q

Dividend payout rate

A

fraction of the company’s earnings which is used for paying dividends

Divt= earnings/shares outstanding * dividend payout rate

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109
Q

What two things can a company do with its earnings?

A

Payout to investors

retain it and reinvest

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110
Q

Change in earnings =

A

new investment * return on new investment

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111
Q

new investment =

A

earnings * retention rate

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112
Q

retention rate

A

the fraction of earnings that the company retains

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113
Q

earnings from growth

A

retention rate * return on new investment

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114
Q

If a firm keeps its retention rate constant…

A

then the growth rate in dividends will equal the growth rate of earnings

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115
Q

What does cutting the firms dividend depend on?

A

the rate of return on the new investment

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116
Q

Limitations to the dividend discount model

A

uncertainty with forecasting a firm’s dividend growth rate and future dividends

small changes in the assumed growth rate can affect the stock price greatly

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117
Q

Share repurchase

A

firm uses excess cash to buy back shares but….

the more cash firms use to rebuy stocks the less it has to pay dividends

EPS increases

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118
Q

Dividend discount model

A

PV0=PV(Future dividends per share)

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119
Q

Total payout model

A

Value of all the firms equity per share

PV0= PV(future total dividend + repurchases)/shares outstanding

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120
Q

Discount free cash flow model

A

determines the total value of a firm to all investors

Enterprise value V0=PV(future free cash flows of firm)

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121
Q

Free cash flow

A

cash flow available to pay both debt holders and equity holders

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122
Q

Enterprise value

A

market value of equity+debt - cash

value of owning the unlevered business

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123
Q

Share price

A

P0=V0+cash0-debt0/Shares outstanding

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124
Q

Present value of dividends payments can determine…

A

Stock price

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125
Q

Present value of total payments can determine…

A

equity value

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126
Q

Present value of free cash flow can determine

A

enterprise value

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127
Q

Valuation based on comparable firms

A

can estimate the value of a firm based on the value of comparable firms or investments with similar cash flows

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128
Q

Valuation multiple

A

ratio of the value to some measure of the firms scale

analogous to floor space pricing if confused

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129
Q

Price earnings ratio

A

Share price/Earnings per share

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130
Q

Trail earnings

A

earnings over the last 12 months

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131
Q

Forward earnings

A

expected earnings over the next 12 months

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132
Q

firms with high growth rates should….

A

have high P/E raitos

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133
Q

Other multiples

A

Multiples of sale
Price to book value of equity per share
enterprise value per subscriber

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134
Q

Limitations of multiples

A

When comparing there is no guidance about how to adjust for differences in future growth rates or risk. Only provides information of firm relative to others. Doe not tell us if the whole sector is overvalued

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135
Q

Discount cash flow methods can be…

A

more accurate than valuation multiples as they can incorporate specific information about the firms cost of capital or future cash flows

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136
Q

Efficient market hypothesis

A

Securities will be fairly priced, based on their future cash flows, given all information that is available to investors

Securities with same equivalent risk should have same expected return

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137
Q

Public, easily interpretable information means….

A

All investors can determine the effect of the information on a firms value

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138
Q

Private or difficult to interpret information means…

A

only a small number of investors may be able to profit by trading on their information (that they will have gathered from their own research). If trade opportunities are large more will devote time to finding alternative resources
The efficient market hypothesis does not hold but as traders trade then the prices will begin to change

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139
Q

Consequences for investors

A

if stocks are fairly priced, investors who buy stocks can expect future cash flows that fairly compensate them for their investment
average investor can invest with confidence

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140
Q

Implications for the corporate managers

A

Focus on NPV and future cash flows
avoid accounting illusions and focus on free cash flows
use financial transactions to support investment

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141
Q

Probability distribution

A

when an investment is risky, there are different returns in may earn and a probability associated with them

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142
Q

Expected return

A

weighted average of the possible returns

E[R] = Σp * R

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143
Q

Variance

A

expected square deviation from the mean

Var(R) = Σp * (R-E[R])^2

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144
Q

Standard deviaition

A

also known as the volatility

square root of variance

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145
Q

Realised returns

A

return that actually occurs over a particular time period

Rt+1 = (Divt+1 + Pt+1 - Pt)/ Pt

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146
Q

If a stock pays dividends at the end of each quarter what is the realised annual return?

A

1+Rannual = (1+RQ1)(1+RQ2)(1+RQ3)(1+RQ4)

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147
Q

Average annual Return

A

If Rt is the realised return of a security in year t, then for the years 1 through T the average return is….

Rbar = 1/T ΣRt

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148
Q

Variance estimate using realised returns

A

1/T-1 Σ(Rt-Rbar)^2

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149
Q

standard error

A

statistical measure of degree of estimator error

SD/root(no. of obs)

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150
Q

95% confidence interval

A

historical average return + or - 2 SE

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151
Q

Excess returns

A

Difference between the average return for an investment and the average return for t-bills

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152
Q

Independent risks

A

related to firm specific news. Diversified, unsystematic

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153
Q

Common risk

A

market wide news related risk/ Also known as undiversified or systematic

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154
Q

When stocks are combined in a portfolio what happens to the risk of the stock

A

the risks will average out and be diversified. Systematic risk will affect all firms and not be diversified. Therefore, volatility will decline until all that remains is systematic risk

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155
Q

The risk premium for diversifiable risk is….

A

Zero. investors are not compensated for holding stocks with firm-specific risk. The can eliminate this for free by diversifying their portfolio

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156
Q

Risk premium for a security is determined by…

A

the systematic risk

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157
Q

Why is volatility not a good way of determining a risk premium?

A

It includes diversifiable risk in the value. We need to determine how much of the volatility is down to systematic risk

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158
Q

An efficient portfolio

A

A portfolio that contains only systematic risk. The only way to reduce the risk of this portfolio is by decreasing the expected returns

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159
Q

Market portfolio

A

An efficient portfolio that contains all shares and securities in the market

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160
Q

What is β?

A

Measure the sensitivity to systematic risk. It is the expected percentage change in the excess return of a security for a 1% change in the excess return in the market portfolio

161
Q

Market risk premium

A

difference between the expected return of the market portfolio and the risk free interest rate

Market risk premium = E[Rmkt)-rf

162
Q

Cost of capital

A

also known as the Capital Asset Pricing Model

E[RI] = rf + β(E[Rmkt] - rf)

163
Q

Portfolio weights

A

the fraction of total investment held in each individual investment

xi = value of investment/total value of portfolio

164
Q

Return of a portfolio

A

weighted average of returns on the investment in the portfolio where weights correspond to portfolio weights

ΣxiRi

165
Q

Expected return of portfolio

A

Σxi * E[Ri]

166
Q

Volatility of a two stock portfolio

A

by combining the stocks we diversify the risk
the amount at which the risk is eliminated is depends on the extent at which they share common risks and prices move together

167
Q

Covariance

A

the expected product of to returns from their means

positive = they move together
negative = they move in opposite direction
168
Q

Correlation

A

measures the common risk shared by stocks that doesnt depend on it volatility

= cov(Ri,Rj)/SD(Ri)SD(Rj)

169
Q

Variance of a two stock portfolio

A

x1^2Var(R1)+x2^2Var(R2)+2x1x2cov(R1,R2)

170
Q

volatility of a large portfolio

A

the variance of a large portfolio is equal to the weighted average covariance of each stock with the portfolio

171
Q

A positive investment in a security is called

A

long position

172
Q

Investing a negative amount in a stock…

A

Short position. sell a stock you dont own and buy it back later

173
Q

Efficient frontier

A

the combination of efficient portfolio combinations.

174
Q

how can risk be reduced in a portfolio?

A

By investing a proportion in risk free investments such as T-Bills. This will, however, also reduced the expected return of the portfolio

175
Q

Levered portfolio

A

the action of an aggressive investor who borrows money to be able to invest more

176
Q

Expected return on a portfolio which is a mixture of risky and risk free investment

A

E[Rxp]= (1-x)rf +xE[Rp] = rf + x(E[Rp] - rf)

177
Q

The standard deviation of a mix portfolio

A

xSD(Rp)

178
Q

How do we find the highest possible expected return for any level of volatility

A

Find the portfolio that generates the steepest possible line when combined with the risk free investment

179
Q

Sharpe Ratio

A

measures the ratio of reward to volatility provided by a portolio

E[Rp]-rf/SD(Rp)

180
Q

Tangent Portfolio

A

the portfolio with the highest sharpe ratio, where the line with the risk free investment is tangent to the efficient frontier of risky investments.
Combination of the risk free asset and the tangent portfolio provide the best risk and return trade off.

The tangent portfolio is efficient

181
Q

conservative investors

A

will invest a small amount in the tangent portfolio

182
Q

aggressive investors

A

will invest more in the tangent portfolio

183
Q

What does the Capital asset pricing model allow us to do?

A

identify the efficient portfolio of risky assets

184
Q

What is the first assumption of CAPM?

A

Investors can buy and sell all securities at competitive market prices and can borrow and lend at the risk free interest rate

185
Q

What is the second assumption of the CAPM?

A

Investors only hold efficient portfolios of trade securities (portfolios that yield the maximum return for a given level of volatility)

186
Q

What is the third assumption of the CAPM?

A

Investors have homogeneous expectations regarding the volatilities, and expected returns of securities

187
Q

What does the demand of the market portfolio equal?

A

the supply of market portfolio

188
Q

When CAPM assumptions hold, what is the optimal portfolio?

A

Is a combination of the risk free investment and market portfolio

189
Q

What is the line called when the tangent line goes through the market portfolio?

A

the capital market line

190
Q

CAPM expected return

A

E[Ri] = rf + βmkt(E[Rmkt] - rf)

191
Q

CAPM beta

A

β = Cov(Ri,Rmkt)/Var(Rmkt)

192
Q

CAPM: Beta of a portfolio

A

weighted average of securities in the portfolio

βp=Σxiβi

193
Q

Market capitalisation

A

total market value of a firms outstanding shares

MV = (no. of shares outstanding)(price per share)
= Ni x Pi

194
Q

Value weighted portfolio

A

A portfolio in which each security is held in proportion to its market capitalisation

xi = market value of i/ total market value of all securities

MV/ΣMV

195
Q

Market indexes

A

particular portfolios of securities.

examples:
S&P 500
Wilshire 500
Dow Jones

196
Q

Drawbacks of using historical data

A

Standard errors of the estimates are large

backward looking may not reflect current expectations

197
Q

Beta corresponds to…

A

the best fitting line in the securities excess returns vs the market excess return

198
Q

what is the purpose of the linear regression?

A

identifies the best fitting line

Ri-Rf = αi + βi(Rmkt - rf) + ei

199
Q

What does the alpha represent in the linear regression?

A

it is the intercept of the regression and is the distance from the security market line : risk - adjusted permance measure for historical returns

200
Q

When α > 0 what does this indicate?

A

the stock has performed better than predicted by the CAPM

201
Q

When α<o what does this indicate?

A

the stock’s historical return is below the security market line

202
Q

Stocks Alpha

A

difference between expected and required return according to the security market line

αs = E[Rs] - rs

203
Q

When the market portfolio is efficient….

A

all stocks are on the SML

All stocks have α = 0

204
Q

If the market portfolio is inefficient how can investors improve the market portfolio

A

buying stocks with positive α and selling stocks with negative α

205
Q

Rational expectations

A

all investors can correctly interpret and use their own information as well as information inferred from market prices or trades of others

206
Q

What is the average portfolio of all investors?

A

is the market portfolio and therefore average α = 0

207
Q

When can the market portfolio be inefficient?

A

if investors misinterpret information and believe they are earning a positive alpha when it is negative

in investors are willing to hold inefficient portfolios

208
Q

Familiarity bias

A

investors favour investments in companies that they are familiar with

209
Q

relative wealth concerns

A

care more about portfolios relative to their peers

210
Q

excessive trading

A

a tremendous amount of trading occurs each day while according to investors CAPM investors should hold

211
Q

Overconfidence bias

A

investors believe they can pick winners when in fact they cannot

212
Q

Sensation seeking

A

An individuals desire for novel and intense risk taking experience

213
Q

If individuals depart from CAPM what happens

A

the departures tend to cancel out, individuals will hold Market portfolio in aggregate will be no effect on market price or returns

214
Q

Disposition effect

A

when an investor holds on to stocks that have lost their value and sell stocks that have risen in value since time of purchase

215
Q

Investor attention as a systematic trading bias

A

individuals are more likely to invest in stocks that have been subject to media attention, experienced high trading volume or have more extreme returns

216
Q

effect of mood on trade of stocks

A

if it is sunny more likely to be happy and thus stock returns are higher

217
Q

experience as a systematic trading bia

A

investors consider own experience rather than historical evidence

218
Q

Herd behviour

A

when investors make similar trading errors because they are actively trying to follow each others behavious

219
Q

informational cascade effects

A

when investors ignore own information hoping to profit from others

220
Q

Implications of behavioural bias

A

engaging in strategies that earn a negative α

superior past performance is not a good predictor of a funds future ability to outperform the market

221
Q

size effect

A

small market stocks earned higher average returns than the market portfolio even after accounting for their betas

stocks have historically earned higher average returns than low book to market stocks

222
Q

momentum strategy

A

buying stocks that have had past high returns and selling stocks that have had past low returns

223
Q

Implication of positive α trading strategy

A

only way positive α strategies can persist in a market is if some barrier to entry restrict competition

224
Q

proxy error

A

true market portfolio may be efficient but proxy used for it may be inaccurate

225
Q

Expected return of marketable security

A

E[R] = rf +βeff (E[Reff] - rf)

226
Q

Self financing portfolio

A

constructed by going long in some projects and short in other stocks with equal market value

the weights sum to zero

E[Rs] = rf + Σβ E[Rf]

227
Q

Market capitalisation strategy

A

small minus big portfolio SMB

228
Q

Book-to-market ratio strategy

A

high- minus-low portfolio HML

229
Q

Past returns strategy :

A

the prior one year momentum PR1YR

230
Q

Fama-French-Cahart factor specifications

A

E[Rs] = rf + βmkt (E[Rmkt]-rf) + βsmb(E[Rsmb - rf) + βhml(E[R] - rf) + βpr1yr(E[Rpr1yr - rf)

231
Q

The FFC compared to CAPM

A

it does no better at measuring risk of actively managed mutual funds

232
Q

Balance sheet

A

list of firms assets and liabilities providing a snapshot of financial position of the firm

233
Q

Assets

A

Liabilities +equity

234
Q

networking capital

A

current assets - current liabilities

235
Q

Book Value of equity

A

BV of assets - BV of liabilities

236
Q

Liquidation Value

A

value once all assets sold and liabilities paid

237
Q

Debt to Equity ratio

A

Total debt/total equity

238
Q

Capital struture

A

mixture of debt and equity

239
Q

traits of debt

A

Not an ownership interest
creditors do not have voting rights
Interest considered cost of doing business and tax is deductible
creditors have legal recourse if payments are missed
excess debt can lead to financial distress and bankruptcy

240
Q

Equity

A

ownership interest
common stockholders vote for the board of directors and other issues
Dividends are not a cost of doing business and are not tax deductible
Dividends are not a liability and stockholders have no recourse if dividends are not paid
An all equity firm cannot go bankrupt

241
Q

Perfect capital markets

A

Investors can trade the same set of securities at competitive market prices
No taxes
No transaction costs
No issuance cost

Financing decisions do not change cash flows or reveal new information

242
Q

Modigliani-Miller Proposition 1

A

In a perfect capital market the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure

243
Q

Unlevered equity

A

is equity in a firm with no debt outstanding

244
Q

Levered equity

A

is equity in a firm with debt

245
Q

market value balance sheet

A

a balance sheet where
all assets and liabilities of the firm are included (even intangible assets such as reputation, brand name, or human capital which are missing from standard accounting)
all values are current market values rather than historical costs

MV Equity + MV Debt = MV assets = MV unlevered equity

246
Q

What effect does leverage have?

A

Will not affect total value of the firm but changes allocation of cash flows between debt and equity without altering total cash flows

247
Q

What effect does debt have on equity?

A

Debt increase the risk of equity

248
Q

Homemade leverage

A

If investors prefer an alternative capital structure to the one the firm has chosen, investors can borrow or lend their own and achieve the same result

249
Q

How can holding unlevered equity be replicated

A

by holding a portfolio or firms equity and debt

250
Q

Leveraged recapitalisation

A

When a firm borrows funds to pay a large special dividend or repurchase a significant amount of outstanding shares

251
Q

The return on unlevered equity

A

ru is related to the returns of levered equity rE and debt rD

E/E+D *rE + D/E+D *rD = rU

rE = rU + D/E(rU - rD)

252
Q

Modigliani- Miller proposition 2

A

The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio

253
Q

As D/E changes

A

rA (return of assets) is constant

the equity cost of capital changes

254
Q

If a firm is unlevered….

A

all free cash flows generated by its assets are paid out to its equity holders

ru = rA

255
Q

If a firm is levered

A

the free cash flows generated by its assets are paid out in to its debt and equity holders in proportions equal to the fraction of the firms value financed

ru = rwacc = E/E+D *rE + D/E+D *rD

if the firms structure is made up of multiple securities then the WACC is calculated by computing the weighted average cost of capital of all the firm’s securities

256
Q

Unlevered beta

A

measure of the risk of a firm as if it did not have leverage which is equivalent to the beta of the firms asset

βu = E/E+D*βE + D/E+D * βD

Leverage amplifies the market risks of a firms assets βu by raising the market risk of equity

257
Q

Conservation of value principle

A

With perfect capital markets transactions neither add nor destroy value but would instead represent a repackaging of risk

value only created by real assets
Any market transaction the appears to e a good deal may be exploiting some type of market imperfection

258
Q

What is the reality of the market and capital structure?

A

Capital structure matters
the irrelevance result serves as a bench mark
Often investors cannot undertake the same financial transactions as firms due to transaction costs, taxes and information asymmetry

259
Q

When do corporations pay taxes on profits?

A

The pay them after interest payments are deducted

Interest expenses reduce the amount of corporate taxes made

260
Q

Interest tax shield

A

reduction in tax paid due to the tax deductibility of interest
The cash flows a levered firm pays to investors will be higher than they would be without leverage by the amount of the interest tax shield

261
Q

Modigliani proposition 1 with taxes

A

The total value of a levered firm exceeds the value of the firm without leverage due to the present value of tax savings from debt

VL = VU + PV(Interest tax shield)

262
Q

If firms borrow a debt and keeps it permanently how can we treat the tax shield?

A

As a perpetuity

PV(Tax shield) = (tax rate * Interest)/rf

263
Q

With tax deductible interest what is the effect after tax borrowing rate?

A

rD(1-taxrate)

264
Q

What happens to WACC in the presence of tax

A

WACC will decline with tax

rWACC = E/E+D *rE +D/E+D *rD (1-taxrate)

by expanding the brackets on the last term we then get

pre-tax WACC - D/E+D rDtaxrate

265
Q

Modigliani miller proposition 2 with taxes

A

The equity cost of caital in the presence of corporation taxes is

rE = rU + (D(1-taxrate)/E)(rU-rD)

266
Q

When are cash flows to investors taxed?

A

They are taxed twice. First at the corporate level and again when they receive the interest payment or dividend.

267
Q

Personal taxes

A

Interest payments received from debt are taxed as income
equity investors also must pay taxes on dividends and capital gains
There are however different types of investors Personal, Institutional, tax exempt, internation

268
Q

When will a firm be indifferent between issuing equity or debt?

A

If

1-taxratei) = (1-taxratec)(1-taxrateE

269
Q

Effective tax advantage of debt

A

taxrate* = 1 - [(1-taxratec)(1-taxrateE)/(1-taxratei)]

270
Q

The value of a levered firm with tax

A

VL = Vu + taxrate* D

271
Q

If taxrate* >0 what does this indicate?

A

Tax advantage of debt

272
Q

If taxrate* < taxratec

A

benefits of leverage reduced due to personal taxes

273
Q

Determining actual tax advantage of tax

A

capital gains taxes are only paid once investor sells stock and realises the gain and loss can be used to offset gains
Income tax rates vary for individuals
Many investors pay no personal taxes

274
Q

When corporate taxes are introduced what happens to the the firms value?

A

It increases with the D/E ratio

275
Q

What do personal taxes and cost of financial distress favour?

A

Equity

276
Q

Limits to the tax benefits of debt

A

to receive the full tax benefits of leverage, the firm does need to have high taxable earnings

277
Q

What is the optimal level of leverage from a tax saving perspective?

A

the level such that interest equal EBIT

278
Q

Financial distress

A

when a firm has difficulty meeting its debt obligation

279
Q

Default

A

when a firm fails to make the required interest or principle payments on its debt, or violates a debt covenant

280
Q

Equity financing

A

does not carry default risk - not legally obligated

281
Q

The risk of bankruptcy

A

is an important consequence of leverage. A firm does not default as long as market value of its assets exceeds its liabilities

282
Q

How does bankruptcy shift ownership?

A

from the firms equity holders to debt holders without changing the total value available to investors

283
Q

Bankruptcy in reality

A

never simple or straightforward!

284
Q

Prepackage Bankruptcy (Prepack)

A

method for avoiding many direct costs of bankruptcy in which a firm first develops a reorganisation agreement with its main creditors and then files for Chapter 11 to implement the plan

  • this is handled quickly and with minimal cost
285
Q

Indirect costs of financial distress

A 
Other costs that can arise among financially distressed firms which may never actually go bankrupt
They are difficult to measure but are greater than direct costs
-loss of customers
-loss of suppliers
-loss of employees
-loss of receivables
-Fire sale of assets
-Delayed Liquidation
-Cost to creditors
286
Q

What two important things should we consider when estimating indirect costs?

A

Loss to firms value

incremental losses due to firms economic distress

287
Q

Who bares the brunt of bankruptcy costs?

A

equity holders

288
Q

Trade off theory

A

Firms pick a capital structure by trading off the benefits of the tax shield against costs of financial distress

289
Q

Modigliani Miller proposition 1 with taxes and bankruptcy

A

Total value of a levered firm

VL = VU + PV(Interest tax shield) - PV(financial distress)

290
Q

US bankruptcy code

A

creditors treated fairly and value of assets not needlessly destroyed

291
Q

2 forms of bankruptcy protection

A

Chapter 7

Chapter 11

292
Q

Chapter 7 bankruptcy

A

Liquidation

A trustee is appointed to oversee the liquidation of the firms assets through an auction
proceeds from the sale of the assets goes to pay firms creditors. The firm then ceases to exist

293
Q

Chapter 11 Bankruptcy

A

All pending collection attempts are suspended
The firms management can propose a reorganisation plan which specifies the treatment of each creditor of the firm
Creditors must vote for to accept the plan and must be approved by bankruptcy court
If an acceptable plan is not reached the court can force chapter 7

294
Q

Direct costs of bankruptcy

A

They are related to the legal process involed in reorganising the bankrupt firm

  • legal expenses
  • advisory fees
  • time that management and creditors spend working out the situation and negotiating
295
Q

Average direct cost of bankruptcy

A

3-4% of the firms pre-bankruptcy market value of total assets

Given these costs firms may avoid filing for bankruptcy by first negotiation with creditors

296
Q

Workout

A

method for avoiding bankruptcy in which a firm in financial distress negotiates with creditors to reorganise

297
Q

Three factors that determine the present value of financial distress

A
  1. the probability of financial distress
  2. the magnitude of the cost after a firm is in financial distress
  3. Discount rate for the distress costs
298
Q

Probability of financial distress

A

Increases with the amount of liabilities

Increases with the volatility cash flows and assets

299
Q

Magnitude of the costs after a firm is in financial distress

A

depends on the industry….
tech firms will have high costs due to the potential for loss of customers and key personnel, lack of tangible assets that can be easily liquidated
real estate firms likely to have low costs due to their assets being sold easily

300
Q

Discount rate for distress costs

A

depends on the firms market risk
the beta of distress cost has the opposite sign to that of the firms
the higher the firm’s beta, the more negative the beta of its distress cost will be

301
Q

Agency costs

A

costs that arise when there are conflicts of interest between the firms stakeholders

302
Q

Overinvestment problem

A

when a firm faces financial distress, shareholders can gain at the expense of the debt holders by taking a negative NPV project if it is sufficiently risky

303
Q

Underinvestment problem

A

When equity holders choose not to invest in a positive NPV project because the firm is in financial distress and then value of undertaking the investment opportunity will accrue to bond holders rather than themselves

304
Q

Cashing out

A

When a firm faces financial distress shareholders have an incentive to withdraw money from a firm

Leverage can encourage managers and shareholders to act in ways that reduce firm value

305
Q

Two effects of adding leverage to captial structure on share price

A
  1. The share price benefits from the equity holders’ ability to exploit debt holders in times of distress
  2. Debt holders recognise this probability and pay less for the debt when it is issued, reducing the amount the firm can issue to shareholders

Debt holders lose more than shareholders gain from these activities and the net effect is a reduction in the share price

306
Q

Debt covenanats

A

conditions of making a loan in which creditors place restriction on actions a firm can take

  • the help reduce costs
  • hinder management flexibility and have potential to prevent investment in positive NPV opportunities and can have a cost of their own
307
Q

Management intrenchment

A

A situation arising as the result of the separation of ownership and control in which managers may make decisions that benefit themselves at investors expenses
- not in best interest of shareholders rather that of the manager

308
Q

Advantage of leverage

A
  1. Concentration of ownership - allows original owners to maintain an equity stake
  2. Reduction of wasteful investment - avoid the effect of managers empire building. When cash is tight managers run the firm as efficiently as possible. Managers more likely to be fired in financial distress. Creditors provide an additional level of management oversight
  3. Commitment. - cannot risk the possibility of bankruptcy
309
Q

The value of a levered firm with addition of agency costs

A

VL = VU + PV(interest tax shield) - PV(financial distress costs) - PV(Agency costs of debt) +PV(Agency costs of debt)

310
Q

Managemnt entrenchment theory

A

managers choose a capital structure to avoid the discipline of debt and maintain their own job security

311
Q

Asymmetric information

A

when parties have different information

312
Q

credibility principle

A

action speak louder than words

313
Q

signalling theory of debt

A

use of leverage as a way to signal to investors

314
Q

Adverse selection

A

When buyers and sellers have different information

315
Q

Implications for equity issuance

A

the stock price declines on the announcement of equity issue
the stock price rises prior to the announcement of equity issue
firms tend to issue equity when informational asymmetry is minimised

316
Q

Implication for equity structure in info asymmetry

A

managers who perceive the firms equity is underpriced will have a preference to fund investment with retained earnings or debt rather than equity

317
Q

Payout policy

A

The way a firm chooses between alternative way to distribute free cash flow to equity holders

318
Q

Part of payout

A

pay dividend or repurchase share

319
Q

Part of retained earnings

A

increase in cash reserves or invest in new projects

320
Q

Declaration date

A

date on which the board authorises a dividend to be paid

321
Q

record date

A

when a firm pays a dividend, only shareholders on record on this date will receive the dividend

322
Q

Ex-dividend date

A

date, two days prior to record date, on or after anyone buying the stock will not be eligible to receive the dividend

323
Q

Payable date

A

date, generally a month after the record date or which the company sends cheques to it registered shareholders

324
Q

Special dividend

A

one time dividend payment which a firm makes. - larger than a regular dividend

325
Q

Stock split

A

when company issues a dividend in shares of stock rather than cash to its shareholders

326
Q

Open market share repurchase

A

buying shares in the open market

  • represents about 95% of repurchase transactions
327
Q

Tender offer

A

Offer to buy back a specified amount of outstanding securities at a prespecified price over a prespecified period of time
- if shareholders dont tender enough shares the company will cancel the transaction

328
Q

Dutch Auction

A

firm lists different prices and the shareholders indicate how many shares they are willing to sell at each price. The firm then pays the lowest price at which they can buy back a desired number of shares

329
Q

Targeted repurchase

A

purchases from a specific shareholder

330
Q

Greenmail

A

when a firm avoids a threat of takeover by buying out the shareholder, often at a large premium over the current market price

331
Q

Cum-Dividend

A

When a stock trades before the ex-dividend date entitling anyone to the dividend

Pcum = current dividend +PV(future dividend)

332
Q

Ex-dividend

A

After the ex-dividend date, new buyers will not receive the current dividend

333
Q

In a perfect capital market what is the investors preference for distribution of funds?

A

they are indifferent between paying a dividend or share repurchase. If the investor wanted cash then he can raise it by selling shares. and vice versa by using cash to buy shares

334
Q

Modigliani - Miller Dividend policy irrelevance

A

In perfect capital markets, holding fixed the investment policy of a firm, the dividend policy is irrelevant and does not effect the initial share price.

The firms free cash flows determines the level of payouts that it can make to its investors

335
Q

Dividends and tax

A

dividends are typically taxed at a higher rate than capital gains.

Shareholders pay lower taxes if a firm uses share repurchase rather than dividends

This repurchase will increase the value of the firm

336
Q

Optimal dividend policy with taxes

A

Pay no dividends at all

337
Q

Dividend puzzle

A

when firms continue to issue dividends despite their tax disadvantage

338
Q

Effective dividend tax rate

A

taxrated* = (taxrated - taxrateg)/(1-taxrateg)

339
Q

What does the effect dividend tax rate measure

A

the additional tax paid by the investor per dollar of after tax capital gains income received as dividend instead

340
Q

Clientele effect

A

when dividend policy reflect the tax preferences of its investor clientele

Individuals in high tax bands prefer low dividend paying stocks

341
Q

Dividend capture theory

A

Absent transaction cost, investors can trade shares at the time of dividend so that non taxed investors receive the dividend

342
Q

Modigliani miller payout irrelevance

A

In perfect capital markets, if a firm invests excess cash flows in financial securities , the firm’s choice of payout versus retention is irrelevant and does not effect initial share price

343
Q

Consequences of retaining cash

A
  1. Reduces cost of raising capital in the future
  2. Increases taxes - retained earnings are taxed twice
  3. Increases agency costs - managers may use the funds inefficiently and increase financial distress costs
344
Q

Dividend smoothing

A

practice of maintaining relatively constant dividends

345
Q

when will firms raise dividends?

A

When they perceive a long term sustainable increase in the expected level of future earnings and only cut them as a last resort

346
Q

Dividend signalling hypothesis

A

Dividned changes reflect the manager’s view about a firms future earning prospects.

347
Q

Signals when a firm increases the dividend

A

positive signal to investors for the foreseeable future
or
signal lack of investment opportnities

348
Q

Signals when a firm decreases the dividend

A

signal management has given up hope that earning will rebound in the near term
or
signal of new positive NPV investment opportunities

349
Q

Signal of a share repurchase

A

the shares are underpriced because if they were overpriced a share repurchase would be costly to shareholders

350
Q

Characteristics of a stock dividend.

A

a firm does not pay out cash to shareholders
total market value of the firm is unchanged
the stock price will fall as same price over a larger number of shares…
not taxed

351
Q

Characteristics of a stock dividend

A

keeps share price within a range
if share prices are too high would be hard for small investors to invest
keeping the price low increases the demand and liquidity and thus boosting the price

352
Q

reverse split

A

when the price of a company’s stock falls too low so company reduces the number of outstanding shares

353
Q

Spin off

A

When a firm sells off a subsidiary by selling shares in that alone

it avoids transaction costs associated with a subsidiary sale

354
Q

Financial option

A

contract that gives the owner the right (but not obligation) to purchase or sell an asset at a fixed price at some future date

355
Q

Call option

A

Gives owner the right to buy an asset

356
Q

Put option

A

Gives the owner a right to sell an asset

357
Q

Exercising option

A

when an option holder buys or sells a share of stock at the agreed upon price

358
Q

Strike price/exercise price

A

price at which an option holder buys or sells a share of stock when the option is exercised

359
Q

Expiration date

A

last date at which an option holder has the right to exercise the option

American option: allow holders to exercise on any day up to and including the expiration date

European Option: can only exercise on the expiration date

360
Q

The option buyer (holder)

A

holds right to option

has a long position in the contract

361
Q

The option seller(writer)

A

sells the option

has a short position in the contract

362
Q

Open interest

A

total number of contracts of a particular option that have been written

363
Q

At-the-money

A

an option whose exercise price is equal to the stock price

364
Q

In-the-money

A

an option whose value if immediately exercised would be positive

365
Q

Out-of-the-money

A

an option whose value if immediately exercised would be negative

366
Q

Deep-in-the-money

A

an option which is in the money and the strike price and stock price are far apart
similar with deep-out-of-the-money

367
Q

Long position on a call option

A

The value of a call option at expiration

C = max(S-K,0) s eing the stock price, K is the strike price

368
Q

Long position on a put option

A

The value of a put option at expiration

P = max(K-S,0)

369
Q

Short position in an option contact

A

An investor that sells an option has an obligation
The seller takes the opposite side to the investor who bought the option
The seller’s cash flows are negative of that of the buyer’s

370
Q

Profits for holding an option until expiration

A

Payouts on a long position in an option contract are never negative. The profit from purchasing an option and holding it to expiration could be negative because of the payout at expiration might be less than the initial cost of the option

371
Q

Characteristics of a call option

A

the maximum loss is 100%
out-of-the-money call options are more likely to expire worthless but if it goes up then it is more likely to have a higher return

372
Q

Characteristics of a put option

A

the maximum loss is 100%
put options will have higher returns in states with low stock prices
put options are not generally held as an investment but as insurance to hedge other risk in a portfolio

373
Q

How can portfolio insurance be achieved/

A

Purchase a stock and a put

or

Purchase a bond and a call

374
Q

Put call parity

A

by the law of one price the payoffs of both combinations of stock and put and call and bond must be the same and they have the same price

S+P=PV(K)+C

375
Q

Price of a european call option for a non-dividend paying stock

A

C = P+S-PV(K)

376
Q

If the strike price K goes up what happens to the price of the call and put?

A

Call goes down Put goes up

377
Q

If the stock price S goes up what happens to the price of the call and put?

A

call goes up put goes down

378
Q

A put option cannot be worth more than…

A

its strike price

379
Q

A call option cannot be worth more than..

A

the stock itself

380
Q

An american option cannot be worth less than…

A

its intrinsic value

381
Q

An american option cannot have a….

A

neegative time value

382
Q

Intrinsic value

A

amount by which an option in in-the-money or zero if it is out-of-the-money

383
Q

Time value

A

difference between an option’s price and its intrinsic value

384
Q

The value of an option increases with what?

A

the volatility of the stock

385
Q

The price of any call option on a non-dividend paying stock….

A

always exceeds the intrinsic value

It is never optimal to exercise a call option on a non-div stock early
It may however be optimal to do this for a put

386
Q

Call option with a dividend paying stock

A

C=S-K+dis(K)+P-PV(div)

387
Q

Put option with a dividend paying stock

A

P= K-S+C-dis(K) +PV(div)

388
Q

Debt as an option portfolio

A

Debt owners can be viewed as owners of the firm having sold a call option with a strike price equal to the required debt payment
Debt can also be viewed as a portfolio of riskless debt and a short position in a put option on the firm’s assets with a strike price equal to the required debt payment

389
Q

Credit default swap

A

Implies we can eliminate a bonds credit risk by buying the very same put option to protect or insure it

Risky debt = Risk-free debt - put options on a firms assets

(rearrange to get risk free debt)

The buyer pays a premium to the seller and receives a payment from the seller to make up for the loss if the bond defaults

390
Q

Agency conflicts

A

Equity is like a call option so equity holders will benefit from risky investments

Debt is a short put option so debt holders will be hurt by an increase in risk

potentially leading to an asset substitution problem

391
Q

If value of assets increases…

A

value of put option will decline

392
Q

Binomial option pricing model

A

A technique used for pricing options based on the assumption that each period the stock return can only take two values

393
Q

Binomial tree

A

A time line with two branches at every date representing the possible events the could happen at those times

394
Q

Replicating portfolio

A

A portfolio consisting of a stock, and a risk free bond that has the same value and payoffs as an option written on the same stock

395
Q

Replicating portfolio in the binomial model

A

Δ = Cu-Cd/Su-Sd

B= Cd-SdΔ/(1+rf)

396
Q

Option price in the binomial model

A

C=SΔ+B

397
Q

Dynamic trading strategy

A

A replication strategy based on the idea that an option can be replicated by dynamically trading in a portfolio of the underlying stock

398
Q

The Black-Scholes option pricing model

A

A technique for pricing european options. when the stock can be trade continuously can be derived from the binomial option pricing model by allowing the length of each period to shrink to zero and letting the number of periods increase infinitely

399
Q

Only 5 inputs are needed for the Black Scholes formula

A 
Stock Price
Strike Price
Exercise date
risk free rate
volatility of the stock

Financial and Capital Markets (1 decks)

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