Financial Markets Flashcards

Question 1

Q

Exam details

Interest

Answer

A

100 % MCQ

Interest

Question 2

Q

When dealing with time value of money, what is the role of interest rate?

Interest

Answer

A

The interest rate is applied to convert time values from one period to another!
- When we need to compare the value of money at different points in time, then we need to apply interest rate. Money received in the future is worth less than the same amout of money receieved in the future. (That’s why more needs to be given back when you borrow).
- To move a cash flow forward in time, you must compound it (Future Value). i.e to determine how much we need to get back without loosing value we compound
- To move a cash flow back in time, we must discount it (Present Value). To determine this lower value we will get in the future, we discount. (this is something you could do if you have debts you will collect in the future but need to show them on your books)

Interest

Question 3

Q

What is compounding?

Interest

Answer

A

Is the process of bringing the present value to the future value (think of it like adding interest so that we know what the value should be in the future when we are not loosing to time-value)

Interest

Question 4

Q

What is discounting

Interest

Answer

A

Is the process of bringing the future value to the present value.

Interest

Question 5

Q

When it comes to borrowing money who is a creditor

Interest

Answer

A

Also known as the lendor.
Is the person who gives out money

Interest

Question 6

Q

When it comes to borrowing money who is a debtor

Interest

Answer

A

Also know n as the borrower
Is the person who borrows the money

Interest

Question 7

Q

What is naming conventions for variables used in borrowing money and calculations

Interest

Answer

A

C0 -> initial cash flow at t0
cn-> cash flow at date n
N-> Date of last cash flow in stream of cashflows. I.e the if payment is due in 10 years then N= date at 10yrs
r -> interest rate or discount rate
t ->

Interest

Question 8

Q

Name 10 kinds of interest rates and their xtics

Interest

Answer

A

Deposit rate ->
Received for deposits at a bank
Debt (borrowing) rate -> Paid for borrowing capital from the bank e.g bank loan
Prime rate -> Interest rate at which banks lend to their most creditworthy clients
Key interest rates or federal funds rate ->
Interest rates at which central banks borrow funds from or lend funds to commercial banks (ECB: see next slide; FED: target federal funds rate)
Money market rates -> (Risk-free) Interest rate on short-term (≈ up to 1 year) transactions
Interbank rates -> Rates at which banks lend to each other
Bond yields -> Yield that can be earned on mid-term and long-term(risk-free) financial instruments
Nominal rate -> Interest rate fixed in financial contracts
Effective rate -> Effective interest rate paid/earned in a financial contract.
Real interest rate -> Yield earned above inflation rate. It’s like the interest you earn minus inflation. FYI, when we fator inflation rates, bond yields could amount effectively to zero.

Interest

Question 9

Q

What are the 3 types of interest rates that apply between banks and central banks?

Interest

Answer

A

Deposit facility: interest on deposit of banks at the central bank which can become negative
Main refinancing rate: publicly visible base rate announced by the central bank
Marginal lending rate: allows financial institutions to borrow money from the central bank on a short-term basis, e.g. overnight

Interest

Question 10

Q

What type of interest rate is being refered to when people talk about govt raising interest rates?

Interest

Answer

A

Main refinancing rate: publicly visible base rate announced by the central bank

Interest

Question 11

Q

What is the longest possible maturity for a German govt bond?

Interest

Answer

A

30 years

Interest

Question 12

Q

What is the yield curve or term structure?

Interest

Answer

A

Is relationship between market price and the remaining time to maturity of a bond.
* the pattern is usually that, the longer the maturity, the highier the yield.
* typically upward slopping
* The longer you invest your money, the highier the yield.

Interest

Question 13

Q

What is a refinancing risk?

Interest

Answer

A

class example. when buying a house, you could get 200k to be paid in 1 year with 3% interest or 200k to payback in 10 years with 20% interest. You choose the later because the former means you might have to take another loan with different rate.

Interest

Question 14

Q

What is the difference / relationship between money markey rates and Bond yields

Interest

Answer

A

Bond yields are mid to long term .ie greater than 1 year
While Money market rates are short term. i.e upto 1 year.
They are both considered risk free.

Interest

Question 15

Q

What is LIBOR and EURIBOR?

Interest

Answer

A

These are fixed rates used for short term lending to banks. they are important because of how they can impact derrrivatives.
* After evidence on LIBOR rigging has emerged, it was decided to phase-out the LIBOR as a benchmark interest rate.
* EURIBOR (published by EMMI at 11 am for 5 tenors by using a panel of 20 large banks) is still in use and important because of its role in derivatives markets

Interest

Question 16

Q

What is the new alternative to LIBOR?

Interest

Answer

A

SOFR - secured overnight financing rate - US
SONIA - sterling overnight index average - UK
ESTER - Euro short term rate - Euro area
SARON - Swiss average overnight rate - swiztland
TONA - Tokyo overnight average rate - Japan

Interest

Question 17

Q

What is a simple interest?

Interest

Answer

A

is One-time interest payment without compounding effect

Interest

Question 18

Q

What is the formula formular

Interest

Answer

A

Cn = Cn-1 + C0r = C0 + (1 + nr)

reverese formular (Present Value) i.e find principle given rate and finanal repayment.
Cn/
(C0+(1+n*r))

Interest

Question 19

Q

How do we deal with interest rates when time period is less than a year?

Interest

Answer

A

Use day count conventions.Examples are
* 30/360 (German method applied for German saving accounts): Every month is considered to have 30 days and every year to have 360 days.
* Actual/360 (French method applied in money markets for short-term lending of currencies): Every month is considered to have the actual number of days, a year is considered to have 360 days.
* Actual/Actual (applied in EURO/U.S. bond markets): Every month and every year are considered to have the actual number of days. Its also called the ICMA rule.

Interest

Question 20

Q

How does the formula for simple interest change when N is less than a year?

Interest

Answer

A

Replace the investment period N by the fraction 4 of the predetermined period:

Cf = C0 + (1 + f*r) where

f = days of investment/days in a year.

fyi: when counting days, count the first day of th getting the money but not the last day paymentn is due. e.g between May 15 and September 16 of the same year means 16 days of interest in May but only 15 days of interest in Sept/.

Interest

Question 21

Q

What is compounding interest rates

Interest

Answer

A

Interest payments are made at the end of the interest period
Assumption: Immediate reinvestment of interest payment at the beginning
of the next interest period
Interest on interest

Interest

Question 22

Q

What is the formula for compounding interest

Interest

Answer

A

Cn = C0 * (1+r)^n
the reverse i.e present value would be
C0 = Cn/((1+r)^n)

Interest

Question 23

Q

What is a zero bond?

Interest

Answer

A

Bond that gives repayment at the maturity because there is not interest in between.

Interest

Question 24

Q

What is compounding frequency and give some examples in life

Interest#intraYearInterest

Answer

A

after how long does compounding happen. represented as (m)

- Morgage payments are usually on monthly compounding frequncy (m=12).
Savings account is usually annual
Current account in Germany: quarterly interest payments (m = 4)
Loan accounts in Germany: monthly interest payments (m = 12)
Saving accounts: yearly interest payments (m = 1)

Interest#intraYearInterest

Question 25

Q

What is effective interest rate?

Interest#

Answer

A

Problem: In contracts interest rates are typically stated on an annual basis. This is called the nominal interest rate (r). However, compounding often takes place on monthly or quarterly intervals.

reff = (1 + r/m)^m - 1

note that.
r/m is interest per compounding period (i.e nominal interest divided by compounding frequency. )

Interest#

Question 26

Q

What is the relationship between nominal interest rate and effective interest rate??

Interest

Question 27

Q

How do you calculate the future value with intra-year interests?

Interest

Answer

A

**Method 1. **
Adjust the interest period to the interest rate
CN = C0 * (1+r/m)^N.

Where
N = Number of interest periods over the entire period
n = Investment period in years,
m = interest periods per year
Meaning N = m* n

Method 2
Adjust the interest rate to the interest period
Cn = C0 * (1+reff)^n

where we already know that
reff = ((1 + r/m)^m) - 1

Interest

Question 28

Q

What is the effect on effective interest rate when compounding happends more than once a year?

Interest

Answer

A

It increases. in the past banks used this to hide highier interests

Interest

Question 29

Q

What is the EU law According to Art. 30, Directive EU 2023/2225 on consumer loan?

Interest

Answer

A

Consumer loan contracts have to disclose the effective interest rate of the loan

and
The way how the effective interest rate is calculated follows the ICMA rules

Interest days are calculated according to the actual/actual rule
All payments associated with the contract have to be accounted for

For consumer mortgage loans similar rules can be found in Art. 17, Directive 2014/17/EU
In Germany, these rules have been transformed into national law with the Preisangabenverordnung (PangV)

Interest

Question 30

Q

What is a consumer loan?

Interest

Answer

A

examples:
mortgage, car loans,

Interest

Question 31

Q

Given an effective interest rate, can we find the monthly (or other) by dividing?

Interest

Answer

A

no, we cant because of compounding. we have to calc each payment separate to find effective interest rate at each period.

Division only works for norminal interest rate.

Interest

Question 32

Q

What is continous compounding?

Interest

Question 33

Q

Research: Look up more about effective interest rate and calculation

Interest

Question 34

Q

How do we calculate continous compounding?

Interest

Answer

A

reff = e^r - 1

Interest

Question 35

Q

What are annuities?

Interest

Answer

A

## is constant payment you have to make. e.g a mortgage

Interest

Question 36

Q

Name two types of annuities

Answer

A

Annuity-due
Annuity-immediate

Question 37

Q

With Examples, Explain type: Annuity-due

annuities

Answer

A

Payments are made at the beginning of the corresponding time interval
First payment at 𝑡0, last payment at 𝑡N-1
e.g Rent (is actually not but you get the concept)

Question 38

Q

With Examples, Explain type: Annuity-immediate

annuities

Answer

A

Payments are made at the end of the corresponding time interval
First payment at 𝑡1, last payment at 𝑡N
E.g Mortgage

Question 39

Q

What is the relationship between annuity-due vs annuity-immediate as determined by the ?No-Arbitrage Principle

annuities

Answer

A

𝐹𝑉 𝑜𝑓 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 due = 𝐹𝑉 𝑜𝑓 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 immediate * (1 + 𝑟)

We can refer to (1 + r) as q

Question 40

Q

What are examples of annuities?

annuities

Answer

A

Pay-in over several periods, one final payment
* * Saving plan
* * Life insurance
* * Building loan contract

Pay-in over several periods, multiple final payments
* * Retirement pension

Do more research. Also calssify them into types

Question 41

Q

What is the formular for calcualating value of future annuities (yearly recuring)

annuities

Answer

A

Picture of of page 13 slides _02_Annuities

Question 42

Q

What is FVF (immediate)? and define its formular

annuities

Answer

A

Future Value Factor of Annuity
FVFImmediate = (Q^N - 1) / (Q - 1)

Question 43

Q

What is PVF? and define its formular

annuities

Answer

A

PVF => Present value factor of an annuity

PVF =

Question 44

Q

What is the discount factor of an Annuity and how is it represented?

annuities

Answer

A

Discount factor is => q

and q = (1 + r)

Question 45

Q

What is the formula for Future Value with with annuities-immediate

annuities

Answer

A

FV = C * (Q^N - 1) / (Q - 1)

Where Q = 1 + r
C is the regular payment

Question 46

Q

How can you calculate Future Value of Anuity due when you have Annuity Immediate?

annuities

Answer

A

Anuity due is paid at the begining so you pay one period more.
FVdue = FV immediate * q

or

FVdue = C * Q ((Q^N - 1) / (Q - 1))

Question 47

Q

What is FVF (due)? and define its formular

annuities

Answer

A

FVF is Future Value Factor of Annuity

FVFdue = Q ((Q^N - 1) / (Q - 1))

we use this one if the payments are made when change comes from investing at the begining instead of at the end of period.

Question 48

Q

How can we find the present value of an annuity immediate

annuities

Answer

A

PV = FV / Q^N
can be expanded into
PV = (C*FVF)/Q^N
even further
….. split FVF …. you know the drill
…
Final formalar = PV = C * PVF

Things to remember
* Discounting the future value with r leads to present value.
* We introduce the concept of PVF
* PVF = (Q^N - 1) / (Q^(N+1) - Q^N)

Question 49

Q

How can we find the present value of an annuity due

annuities

Answer

A

PV = FVdue / Q^N
can be expanded into
PV = (C*FVFdue)/Q^N
even further
….. split FVF …. you know the drill
PV = Cdue * (1/Q^N) * …
Final formalar = PV = C * PVFdue

Things to remember
* Discounting the future value with r leads to present value.
* We introduce the concept of PVFdue
* PVFdue = (Q^(N+1) - Q)/(Q^(N+1) - Q^N)

Question 50

Q

What is a perpetuity in annuities?

annuities

Answer

A

Example is a stock held for a very long time. Interest is equal to dividend and the this divident payment can be regarded as an annuity to be paid in perpetuity. i.e N -> Infinity

Question 51

Q

What is the Present Value formula for an annuity paid in perpetuity?

annuities

Answer

A

For annuity Immediate
PV = C/q-1 or
PV = C/r

For Annuity due Not in formula sheet.
PVdue = (q * C) / (q - 1)

remember to look into the derivations

Question 52

Q

What are the 3 possible cases of intra year annuities.

annuities

Answer

A

CASE 1: Annuity period same as interest period. e.g monthly mortgae with monthly compounding interest.
CASE 2: Annuity payments are made intra-yearly, interest payments annually. (This also means multiple annuities are paid out in one interest period)
CASE 3: Annuity payments are made annually,interest payments intra-yearly. (also means multiple interest payments within one Annuity period)
*

Question 53

Q

What are FV formula for case 1: when anuity period == interest period?

annuities

Answer

A

Check page 46 take screenshot

Question 54

Q

What are PV formula for case 1: when anuity period == interest period?

annuities

Answer

A

Check page 46 Annuites lecture

Question 55

Q

CASE STUDY: In the case of a mortgage, what is PV, FV.

annuities

Answer

A

PV
The present value (PV) of a mortgage is the initial loan amount—the amount borrowed from the lender. It is the value today of all the future mortgage payments, discounted at the mortgage interest rate.

FV
The future value (FV) of a mortgage is the total amount of all the payments made over the life of the mortgage, including both principal and interest. For most practical purposes in a mortgage context, we are more concerned with the present value and the periodic payments rather than the future value of the payments.

Question 56

Q

What are PV formula for case 2: when Annuity payments intra-yearly and interest annually

annuities

Answer

A

Check annuities page 50.
Also called Fictitious periodicannuity

NOTES:
- First transform monthly payments into imaginary annual payment C’.

Question 57

Q

What are FV formula for case 2: when Annuity payments intra-yearly and interest annually

annuities

Answer

A

Check annuities page 52.
Also called Fictitious periodicannuity

Question 58

Q

What are PV formula for case 3: when Annuity payments yearly and interest intra-annual

annuities

Answer

A

check page 61.

Notes:
- we create fake intrest rate r’
- we can then use all the regular formulas
- r’ is actually the effective interest rate we learnt before

Question 59

Q

What is geometric progression in annuities?

annuities

Question 60

Q

What is Arithmetic progression in annuities?

annuities

Question 61

Q

What is FV of arithmetic progression in annuities?

annuities

Answer

A

check page 68

Question 62

Q

What is FVdue of arithmetic progression in annuities?
eck

annuities

Question 63

Q

What is FV of geometric progression in annuities?

annuities

Question 64

Q

What is FVdue of geometric progression in annuities?

annuities

Answer 57

A

g = 1 + growth rate

Answer 58

A

Check notes after page 85

Answer 59

A

N -> Infinity
PV exists only if q > g
*

Answer 60

A

Redemption or repayment calculation is about the repayment of an outstanding principal loan amount from the borrower to the lender

Redemptions

Answer 61

A

Scenario in which annuity reoayment remains equal. i.e Annuity is constant rather than the repayment amount.

Notes:
You pay the same amount, part of it goes to intertest, the other to reaying the loan. with time the portiotion of it that goes to interest reduces because the loan left is decreasing and the amount that goes into the repayment is more. look at graph on page 12 redemption slides

Answer 62

A

PV of annuity repayments should be equal to D0
A is D0 * 1/PVC

Answer 63

A

Check formoular on pgae 14. It’s not provided in the sheets

Assumptions
* Payment in period k == payment in period k-1. i.e Ik + Tk = Ik-1 + Tk-1
* simplified. Tk = Tk-1 + Ik-1 - Ik
* Ik and Ik-1 have formulas. sub those
* T1 = …something something

Answer 64

A

Price is in percnetage
No intermediate repayments
Interest is paid annually (can also be other period)
Whole principle is then repaid at end of maturity
Most bonds don’t have collateral
Small companies don’t usually do bonds because it is expensive to list them. they rather do bamk loan

Answer 65

A

US - 20 years
Germany - 30 years
Mexico - 100 years

Notes: do more research

Answer 66

A

Bond price
Credit Worthiness of issuer
Interest rate
Coupon
Rights - e.g right to call the bond
Liquidty - Are there people willling to buy?

Answer 67

A

Coupon Bond: Bond with fixed interest payments over lifetime (coupon payments) and repayment of principle amount at maturity of the bond
Zero-coupon bond (zerobond): Bond without coupon payments with repayment of face value at maturity
Bond with variable interest (Floater): Coupon payments are adjusted to current interest level (LIBOR).
Perpetual / Consol Bond: Bonds without maturity date.
Convertible Bond: Bond with small coupon that provide the possibility to be exchanged against stocks at a predetermined date in time.
Option bond / warrant bond: Follows the idea of a convertible bond, although the option right is traded separately.
Reverse convertibles: The issuer can choose to repay with shares instead of cash.

Answer 68

A

B0 = 100 => Bond is traded at par
B0 > 100 => bond is traded at premium (above par)
B0 < 100 => bond is traded at discount (below par)

Answer 69

A

If Coupon > Interest => traded above par
Coupon < interest => traded below par
coupon = interest => traded at par

Answer 70

A

The buyer needs to pay a compensation to the seller due to the proportionate interest claims the seller has gained.
The buying price will then equal the sum of market price and accrued interests.

Answer 71

A

Interest claims between last interest payment date and selling date are added to the market price of the security
I0 = (t1 - t0) * 1/T * C => screenshot form on pg 16. not in sheet
T are the days in the coupon period
Counting conventions for T used are
30/360: used for bank accounts (German method)
act/360: used on (Euro) money markets (French method)
act/act: used for bonds (ISDA method) - Usually prefered in the bond market

Answer 72

A

For highier maturity: The change in price due to change much highier relative to change in interest. (i.e small change in interest rate can make big change in price e.g 2% change in interest could make 4 % change in price)

For lower maturity: Difference in change is lower, sometimes even negligible. e.g for maturity in a few weeks

NOTE: The direction of the change is also affected by the price of the coupon

Answer 73

A

Yield to Maturity defines the return that will be earned by the bond owner when the bond is held until maturity under the condition that the risk-adjusted market interest rate remains unchanged (re-investment hypothesis).
The Yield to Maturity is denoted per annum (p.a.).

Answer 74

A

The lower the market interest rate, the higher the market price of a bond because the present value of the single payments of the bond increases.

Answer 75

A

Future value of bond is not the same as BN (redmeption Value of the bond at maturity)
The future value is coupon values collected + interests earned on coupons + redemption value.
Check example in notes pg 36 (reader).
Hint, official example shows Summation but we can just take the first part of the B0 formula i.e everything but the multiplication

Answer 76

A

In theory, YTM should be equal to market interest rate but don’t count on this in exams.

To calculate YTM = (NthRoot of (FV / B0)) - 1 . this is not in formula. check notes on page 36

Answer 77

A

Normal yield curve: The longer the capital commitment, the higher the interest which is paid.
Flat yield curve: The paid interest does not depend on the time of capital commitment.
Inverse yield curve: The longer the capital commitment, the lower the interest which is paid.

Answer 78

A

Pure expectation hypothesis
Liquidity preference theory(prefered habitat theory)
Market segmentation theory

Answer 79

A

is Yield to maturity of the risk-free govt bond

Answer 80

A

Is periodic interest rate for period t based on information available in in t = 0

Answer 81

A

fomular not in table
check notes on slide 44

Answer 82

A

example on page 46

Answer 83

A

Credit risk
Price risk due to changes in the interest rate level
Risk of reinvestment (of coupons)

Answer 84

A

the coupon payments at issuance (rating premium)
the risk-adjusted interest rate (discount rate)

NOTES:
which means, it has a direct impact on the market price of a bond.

Answer 85

A

Investment grade: rated AAA, AA, A, BBB
Junk bonds: BB,B, CCC
In default: D

Answer 86

A

Slide 67 - graph. Point D is known as the Duration.
The duration is the average of the payment dates of a security weighted with the corresponding present value proportion.
Duration is also refered to as average commitment period

NOTES:
If market interest rate changes, this affects the value of the bond. But there is a point where that future interest rate will cause an intersection in the price of the bond to projected price based on the innitial rate. this point is called the duration.
For a zero bond: duration is always the same as the maturity. because we dont receive any in between payments
For coupon: Duration is below maturity but we still have to calculate it.

Answer 87

A

Is How strong does the present value of a bond react to any changes in the interest rate

Answer 88

A

The sensitivity can be approximated by the measure of duration
The higher the duration, the higher the interest sensitivity

Answer 89

A

Flat yield curve
ONE-TIME change of the market interest rate INSTANTLY after the purchase of the bond
Only the level of the yield curve changes, not the slope or the curvature of the curve
Coupon payments are reinvested with the market interest rate r

Answer 90

A

Check slided 77. not in sheets.
Also look at slide 78 ofr other formular
Same slide also shows modified duration. important to note that’s not the same as Duration

Answer 91

A

the longer the time to maturity, the larger the duration.
the lower the market interest rate, the larger the duration
the lower the coupon, the larger the duration. (lower coupon means the bond is more like a zero bond)

Answer 92

A

Dperp = (1+r)/1
check slide 82. not in sheet

Answer 93

A

Stocks represent Equity, bonds represent debt

Answer 94

A

GMBh - 25,000
Stock Corp - 50,000

Answer 95

A

Ownership can be easily exchanged

Answer 96

A

Dividends are the proportion of a company’s earnings which is distributed to the shareholders

Answer 97

A

Cash dividend
Stock dividend (e.g. Deutsche Telekom 2013)

Answer 98

A

Yearly in DE
Quarterly in USA
*

Answer 99

A

When a company pays dividends, the stock price typically decreases by the amount of the dividend on the ex-dividend date.

Answer 100

A

Dividend payments are subject to taxation.
Investors that may get highly taxed may be willing to sell the stock to avoid the heavy tax on dividend
Investors that are tax exempted may opt to pick up the stock to get dividend.
Some countries decide to that dividend is only given if you hold stock for atleast a year.

Answer 101

A

Dividend per share = sum of all dividend payments / Number of shares outstanding

it represents the amount of cash dividends paid to shareholders for each share of common stock they own.
Indication: It shows how much profit a company is distributing to its shareholders versus reinvesting in the business

Dividend yield = Divident per share / Share Price.

It shows how much a company pays out in dividends each year relative to its stock price.
Indication: measure of the income generated by an investment in a company’s shares, expressed as a percentage of the share price.

Payout ratio (dividend ratio) = Dividend per share / Earnings per share.
Is the proportion of a company’s earnings that is paid out to shareholders in the form of dividends.
Indication: How much company is investing back into the businesss. Growth potential.

Answer 102

A

Stock Repurchase
Company buys back shares on the stock market. This news also tends to push up the stock price

Answer 103

A

No.
NOTES: shares held by the company are subtracted when calculating divident per share.
Companies cannot own more than 10% percent of their own shares in EU and Germany. The 10% (or any %age owned) also does not give you voting rights. in other words treated like they dont exist.

Answer 104

A

(EMH) is a financial theory that suggests that financial markets are “informationally efficient,” meaning that asset prices fully reflect all available information at any given time.

According to EMH, it is impossible to consistently achieve higher returns than average market returns on a risk-adjusted basis, because asset prices should only react to new information.

Answer 105

A

The price of a stock should equal the present value of its future cash flows distributed to the shareholder (discounted cash flow principle).

NOTES:
In Reality: The value of a stock can differ from its price which is the result of specific conditions within a specific market environment with non- efficient market mechanisms.
We assume a perfect capital market so that the price of a stock equals its fundamental value.

Answer 106

A

Large number of investors without market power
Equal access to information by all market participants
Completely rational economic actors
No transaction costs (e.g. taxes)

Answer 107

A

Eugene Fama and Richard Thaler represent two divergent views on financial markets. Fama, through the Efficient Market Hypothesis, argues that markets are efficient and rational, while Thaler, through behavioral finance, suggests that markets are often inefficient due to human irrationality and cognitive biases.

Market Efficiency:
- Fama: Markets are efficient and prices reflect all available information. Any deviations from true value are quickly corrected by rational traders.
- Thaler: Markets are not fully efficient because investors are not always rational. Psychological factors and biases can lead to persistent mispricings and anomalies.

Investment Strategy:
- Fama: Passive investing is optimal since it’s difficult to outperform the market consistently.
- Thaler: Opportunities exist for investors to exploit market inefficiencies through active strategies, though they must be aware of their own biases.

Price Behavior:
- Fama: Price changes are random and unpredictable due to the efficient incorporation of information.
- Thaler: Price changes can be influenced by irrational behavior, leading to trends and patterns that can sometimes be predicted.

Answer 108

A

re (return on equity) = ((D1 + P1)/P0) - 1
Check slide 17. not in sheet.

can be re-writen as
P0 = (D1 + P1)/ (1 + re)

Answer 109

A

Check slide 21.

P0 = D1/(1+re) + D2/(1+re)^2 + D3/(1+re)^3 + DN/(1+re)^N ….
N is very very large because stocks unlike bonds, have no maturity.

Answer 110

A

Zero-growthmodel
Constant growth model
Time-varying growth model

Answer 111

A

Slide 23.
P0 = D/re (not in sheet)

NOTES:
Here we assume Constant dividend payments.
The Formula for a perpetual annuity can be applied (constant regular payment at
regular points in time)

Answer 112

A

Slide 23.
P0 = D1/re - w, where D1 = D0 * (1 + w)

Notes:
We assume constant dividend growth by factor 𝒘
Formula for a geometrically growing perpetuity (Gordon growth model)
Important: if asked for dicount rate, you can solve for it with the same formula

Answer 113

A

Relatively low risk (small 𝑟e)
High dividend ratio
Relatively slow growth 𝑤
FYI: A good long-term approximation of firm growth is the country growth since it is, per definition, not possible that a firm always grows with higher growth rates over a long period of time.

NOTES:
For companies which are not mature and which might act in a dynamic market environment we observe non-constant growth rates. Then, we cannot apply the model of constant or constantly growing dividends. We need to account for the fact that we observe time-varying growth rates.

Answer 114

A

Slide 28. not in formula sheet.

It could be two cases:
CASE 1 is is constant growth with factor w untill N and then zero growth after that.
CASE 2 is is constant growth with factor wa untill N and then constant growth with factor wb after that.
Formula combines perpetuity with growth factor 1 and then with growth factor 2. (or no growth if thats the case)

Answer 115

A

All projects with 𝑅𝑂𝐸 > 𝑟# will result a positive net present value
For young firms which act in a new market, there are a lot of these projects
resulting in a high overall return on equity, and a growth rate 𝑤 which can be above the costs of equity
Due to the high profitability other firms enter the market and the number of profitable projects goes down. Moreover, as the company gets larger the potential for further growth decreases.
Then, the firm reaches a constant firm-specific growth rate. The maximum rate equals the overall country-wide growth rate and is smaller than the costs of equity
Over time (in the model of time-varying growth at the transition from one phase to the other), 𝑅𝑂𝐸 and 𝑤 will decrease whereas 𝑝 will increase

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