1
Prof. Dr. Hanno Beck
European financial
markets
Outline of the course
(1) The debt merry-go-round
(2) products, actors and exchanges
(3) Reward, risk and volatility
(4) Pricing
(5) Portfolio Selection
(6) Forecasting
Presentations
(1) Banking and banks:
Admati and Hellwig
(2) Risk: The Black swan
(3) Forecasting: Mandelbrot
(4) Psychology: Belsky / Gilovich
(5) Crises:Kindleberger
2
Session # 1
The debt merry-go-round
Why do we need
capital markets?
6
savings
markets borrowers intermediaries
3
• Capital markets channel funds from sectors that have a surplus of funds (lenders) to sectors with a shortage of funds (borrowers)
• They transform household savings into funds available for investment by firms
• Lender / savers: Individuals (saving for retirement, car-financeetc); companies
• Borrowers:
– Individuals (mortgages, consumption)
– Companies (investments,funding cash flow)
– Governments, municipalities (funding national debt)
– Public corporations
The debt merry-go-round
8
inte
rmed
iari
es
Pension funds
Insurance companies
Private Equity
Hedge Funds
Mutual funds
banks
mark
ets
Stock markets
Bonds markets
Currency m.
derivatives
Electronic communication
networks
Private Placement
borr
ow
ers companies
Start-Ups
hedging
Funding / investing cash
flow
The debt-merry-go-round
savings
• Saving means sacrificing present for future consumption: consumption today is postponed in favor of consumption at some (known or unknown) future point in time
• Why should you save? – consumption today is better than consumption tomorrow
– consumption tomorrow is insecure
• Answer #1: saving for rainy days
• Answer #2: saving for a bigger expenditure (why not take a credit?)
• Answer #3: decreasing marginal utility of consumption
Why do people save?
4
6
65
5
10
Income
4
3
20
2
age
The life-cycle Hypothesis
income
1
consumption
consumption
saving
Lifetime savings period
Dissaving
(retirement)
savings
The life-cycle Hypothesis
0
10000
20000
30000
40000
50000
60000
70000
17 22 27 32 37 42 47 52 57 62 67 72 77 82
Household Consumption Disposable Household Income
DM / Year
1) Mean of 5-Year-Cohorts based on the EV-Sample of the Years 1978, 1983, 1988, 1993
Disposable Household Income and Household Consumption
Dependent on Household Age for Germany1)
• Investing means "using savings to buy production factors”
(=capital goods like production buildings and machines) to
produce goods and services
• The more capital goods used in production, the higher
productivity, i.e. real output of goods and services.
• This increase in real output makes investment “profitable”.
• Consequently, investors are willing to pay a certain amount
of goods and services (=a certain interest rate) for the right
to use savings to buy productions factors.
• However, the productivity of an additional investment
normally decreases with an increase in the volume of
investment.
Why do people invest?
5
• People demand compensation on their savings because – they want compensation for their delay of consumption
– they want compensation for the risk that they loose their money
– they want compensation for the devaluing of their savings by inflation
• With increasing maturity /risk of the investment, lenders demand a higher interest
• no free lunch, i.e. no higher reward without higher risk
• decreasing marginal utility of savings
– once you reach the optimal allocation of your income between consumption today and consumption tomorrow (= optimal level of saving), a further postponement of consumption into the future causes a loss of utility
– to compensate the household for this loss of utility, an investor, who wants the household to save more, has to pay compensation for this loss of utility – i.e., interest
Why do people demand reward?
• Matching lenders and borrowers (allocation of capital)
• Reducing transaction costs:
– Economies of scale: infrastructure, information,
– pooling smaller investments from disparate savers
– evaluating borrowers’ ability to repay the loan (reducing adverse
selection and moral hazard, i.e. information asymmetry)
• Distributing and allocating risk:
– pooling risks upon many shoulders
– risks end up with those who have the highest capacity to bear it
• Providing liquidity, i.e. ease and speed with which agents can
convert assets into purchasing power at agreed prices
– investing in long-term projects for a short term
– E.g.banking: transforming short-term liquid deposits into long-term
illiquid loans
What is the role of capital markets?
Reducing information asymmetry • financial system helps overcome an information asymmetry
between borrowers and lenders
• borrowers know more about their investment projects than
lenders.
• Borrowers most eager to engage in a transaction are the
most likely ones to produce an undesirable outcome for the
lender (adverse selection).
• Individual savers may not have the time, capacity, or means
to collect and process information on a wide array of potential
borrowers.
• Without intermediaries, each investor would face the large
fixed cost associated with evaluating investment projects.
• => high information costs may keep funds from flowing to
their highest productive use =>financial systems are helpful.
6
• Markets offer a broad range of high- and low-risk investment opportunities portfolio shift towards projects with higher expected returns.
• Ability to hold diversified portfolio of innovative projects reduces risk and promotes investment in growth enhancing activities.
• Liquidity = ease and speed with which agents can convert assets into purchasing power at agreed prices.
• Savers are generally unwilling to delegate control over their savings to investors for long periods less investment in high-return projects with long-term commitment of capital.
• Financial system creates possibility to hold liquid assets (equity, bonds, demand deposits) that they can sell quickly and easily if they seek access to their savings, simultaneously transforming these liquid financial instruments into long-term capital investments Without financial system investors would be locked in illiquid long-term investment with high payoffs only to those who consume at the end of the investment.
Trading, diversification and risk
Markets and banks
• Direct finance: a sector in need of funds borrows from
another sector via financial market market based system
• Indirect finance: financial intermediary obtains funds from
savers and uses these savings to market loans to a sector
in need of finance bank-based system
source: ECB
Bank-based or market-based?
Financial Systems of the Member States of the EU:
7
Session # 2
Products
markets borrowers intermediaries
Bonds
Stocks
Funds
Bank credit
Derivatives
Real estate
Alternative
investments
Capital markets: products
• Debt
– lending a fixed sum; promise to repay the sum
– time horizon: depends on individual contract
– Reward: interest (floating or fixed); capital gains if sold before maturity; upside limited
– no voting-rights
– Corporate Bonds, Gilts, Bunds, money-market, T-Bills
• Equity
– part-ownership
– Time-horizon: unlimited unless you don’t sell them
– reward: dividends, capital gains if you sell them, upside unlimited
– voting rights on business-policy (CEO, pay etc.)
Capital markets: products
8
• Derivatives – Payoffs depend on the value of other assets (stocks, bonds, forex,
commodity prices)
– Futures, Options
– Aim: Arbitrage, hedging or speculation
• Real Estate – reward: capital gains, rent
– Inflation-protected
• Alternative Investments – `alternative’ means not correlated with other markets
– commodities (oil, wheat etc.), gold, silver, wood, art etc
– often rather illiquid markets; i.e. higher risk
– small markets
Capital markets: products
Debt
• Money market
– Short-term debt
– T-Bills, certificates of deposits, commercial papers, Repos, Fed Funds
– Yield: LIBOR, rate at which banks in London are willing to lend money
• Bond market – Treasury notes and bonds, TIPS (inflation protected
treasuries)
– corporate bonds
– Secured bonds: backed by assets (mortgages, loans)
– unsecured (debentures), subordinates debentures
• Bank Credit
Products: Debt
9
Stocks
• A stock is a residual claim, i.e. stockholders are last
in line of all those who have a claim on the assets
and income of the corporation
• Limited liability: the most you can loose in the event
of a failure of the company is your initial investment
• daily performance: indices (“the market”)
– price-weighted average of stocks (Dow Jones) vs. value-
weighted indices (S & P-500; DAX)
– other indices: NASDAQ, MSCI-Index-family, Nikkei,CAC-
40; regional indices, sector indices, ethical indices (DJ
Sustainibility index)
– index-tracking (Index-funds, ETFs), i.e. passive investing.
Is it possible to beat the market (active investing)?
Products: Stocks
Advantages of being listed
• So why companies try to be listed (IPO)?
• Increase firms financial autonomy (less
dependency on one financial resource)
• Diversify firms investment risk (by selling
stakes in the company in a liquid market)
• Brand recognition
• Improved transparency
• Price of Companies share ≡ discipline
mechanism for managers
10
Disadvantages of being listed
• Equity issuance is an expensive procedure:
– underwriters' commission
– Legal fees
– other charges resulting primarily from the need to
satisfy the additional disclosure requirements
• Investors’ Point of view:
– Widely Shared ownership of the company
Resulting in larger gap between external
investors and managers (agency problems)
Derivatives
• Can be based on:
– different types of assets (e.g. equities or commodities)
– prices (e.g. interest rates or exchange rates)
– indexes (e.g. a stock-market index)
• Buffet: weapons of mass destruction
• Or: derivatives helps to identify, isolate and
manage the market risk:
– i.e. changes in market prices of financial instruments
– changes in interest and exchange rates
– Derivatives can reduce risks through hedging by
transferring the cost of bearing the risk from one party
to the other
11
Derivatives
• Derivatives advantages:
– helps Portfolio managers to change its risk profile
through derivative transactions at a very low cost.
– are low cost risk assessment tools.
– can be tailor-made in the over-the-counter market.
• Types of derivatives:
– future: forward contract gives the holder the
obligation to buy or sell a certain underlying
instrument (e.g. a bond) at a certain date in the future,
at a specified price.
– Options: options give the holder the right (but not the
obligation) to buy or sell a certain underlying
instrument at a certain date in the future at a specified
price.
• Options vs. futures: an option gives the right to buy/sell a position, a future obliges to buy/sell a position
• Example: price t0: 100, what about price in t1? – Long position: you expect p1 > p0; so buy a call option or
a long position (future), you acquire the right to buy the stock in t1 for a price you agree on in t0. Profit = price agreed on – p1 – cost of option/future. (loss in case of option only the price of the option)
– Short position: you expect p1 < p0; so buy a put option (sell a call) or a short position (future), you acquire the right to sell the stock in t1 for a price you agree on in t0. Profit: price agreed upon – p1 – cost of option/future. Loss in case of option only the price of the option
Derivatives
OTC Derivative markets turnover
12
• Forwards: agreement to borrow / lend a sum of money at an agreed rate for an agreed period starting on a future date. Hedge against interest rate increase
• Swap: exchange e.g. interest rate obligations. After agreeing on a fixed amount, A pays a fixed interest to B who in exchange pays a floating rate to A.
• Caps, floors, collars: products which eliminate the risk of too high / low prices in a certain range
• Credit default swaps: A buys a bond, he buys a CDS from B for a premium. If the bonds defaults, B buys the bond from A at face value; i.e. B bears the risk of a default
Other Derivatives
Markets
• Where are securities being traded?
• Primary markets: first issue of rights; IPO (stocks), public offering (bonds), sometimes private placements.
• Public offerings are marketed be investment banks (underwriters)
• Secondary markets: after issuing, securities are being traded
– over the counter
– Exchanges (dealers offer bid and ask-prices)
– Electronic Communication Networks (Archipelargo), matching orders automatically
– Specialist markets
Capital markets: exchanges
13
Institutional players
• Institutional investors are specialized financial institutions
that manage collectively savings of small investors
• Pension funds: collect, pool, and invest funds contributed by
employers and employees and their family members to
provide for the future pension entitlements of beneficiaries
• Life insurance companies: offer a mix of long-term saving
and insurance products
• Mutual funds: investment vehicles whose underlying assets
are identifiable and are marked-to-market
• Hedge funds: eclectic investment pools, typically organized
as private partnerships
• Private equity: invest in non-public companies and often
finance these investments with a significant amount of debt
14
• Why must governments intervene in capital markets?
• To protect property rights and to enforce contracts.
• To encourage proper information provision (transparency) so
that providers of funds can take better decisions on how to
allocate their money.
• To avoid systemic crises: bank runs and collapses, market
crashes (e.g. by introducing circuit breakers), domino-effects
• To avoid fraud, insider trading, scalping
• Government should arrange for regulation and supervision
of financial institutions in order to ensure their soundness.
• Governments are responsible for competition policy to
ensure competition
The case for regulation
15
• simplify existing legislation
• reduce the administrative burden of legislation
• conduct a cost-benefit analysis before proposing new rules
for better regulation, the
European Commission has embarked on a 3-way program to:
• The current regulatory system in the EU is based on the principle of home country control combined with minimum standards and mutual recognition.
• A financial institution is authorized and supervised in its home country and can expand in the EU by offering cross-border services in other EU Member States or establishing branches in these countries without additional supervision by host-country authorities.
Prudential supervision
Prudential supervision
• Licensing, authorization or chartering of financial institutions
• The on-going monitoring of the health of financial institutions and the financial system (the asset quality, capital adequacy, liquidity, management, internal controls, and earnings)
• Sanctioning or imposition of penalties in case of non-compliance with the law, fraud, bad management or other types of wrongdoing
• Crisis management, which comprises lender of last resort, deposit insurance and insolvency proceedings
prudential supervision a process with four
stages:
Session # 5
Reward, Risk and
volatility
16
• How do we compare different choices
• Features of an investment
– time horizon: how long is the money invested?
– yield
– risk
• To compare different investments, we must describe them in terms of return AND risk
• Return R:
• Beware: this is ex-post-return, i.e., return after the investment is done (and gone?)
Reward, Risk and volatility
Dividends / interest rate payments + price t1 – price t0
price t0
Reward, Risk and volatility
R - p
1 +p
• The longer the investment horizon, the longer the real return
• How to make investments comparable, concerning the time-horizon
• Suppose your investment runs n years, you invest $A and get as return $B, so your annualized return is AR = , effective annual rate (EAR)
Reward, Risk and volatility
17
• All these formulas are computing ex-post-reward, i.e. reward after the investment is finished
• But to invest, you need information about the expected reward, i.e. ex-ante-reward
• Ex-ante-reward depends on the performance of the investment and the probability for that performance
• High reward with low probability vs. low reward with high probability
• How do you take these probabilities into account?
• Pascals wager – shall we believe in god?
• Financial markets turned Pascals calculation into the most-used formula:
Reward, Risk and volatility
Shall we believe in
Santa Claus?
18
believe Believe
not
No Santa
Santa
Risk analysis
safe Not safe
No crash
Crash
A more serious example:
• Three possible outcomes
for a security, what is the
expected value?
• expected value:
weighted average of the
expected payoffs
associated with all
possible outcomes
• i.e.: if our assumptions
about the probabilities
are correct and we
repeat this investment
infinite times, our return
on average would be $4
Event probability stock
price
Boom 1/3 6
Recession 1/3 2
no change 1/3 4
EV = 1/3 *6 + 1/3 *2 + 1/3 *4 = $4
Expected return
19
• Higher variability, i.e., the
extent to which possible
outcomes of an uncertain
event differ means a higher
risk. How do we measure
variability?
• Idea #1: deviations from the
average (i.e., EV). This does
not work because the sum of
deviations from the average
always yields zero!
• Idea #2: squared deviations
yield positive numbers
• Idea #3: take the square root
of #2 to make the squares
disappear again.
Event probability stock
price
Boom 1/3 6
Recession 1/3 2
no change 1/3 4
EV = 1/3 *6 + 1/3 *2 + 1/3 *4 = 4$
#1: 1/3 (-2) + 1/3 (0) + 1/3 (2) = 0
#2: 1/3 (-2)2 + 1/3 (0)2 + 1/3 (2)2 = 2.6
#3: 2.6 1.6$ = Standard deviation
Exel: STABWNA (Field:Field)
What is risk?
• Expected value is what you expect the price of an asset to be on average
• Standard deviation , most times called volatility, is a measure of risk. – average value of deviations from the average
– gives the same weight to positive as well as negative deviations from the average
• EV and are used to describe the probability distribution of the returns
• Most modells in finance assume a bell-shaped probability distribution
Reward, Risk and volatility
• Each column represents
an expected payoff; the
height of each column
represents the probability
of this event
• In the example,
probabilities are evenly
spread over the
alternative outcomes
(Rectangular distribution)
probability
return
1/3
2 4 6
What is risk?
EV = 1/3 *6 + 1/3 *2 + 1/3 *4 = 4$
s = 1.6
A
20
• EV = 1/4 *6 + 1/2 *2 + 1/4 *4 = 3.5$
• SD: 1/4 (-2)2 + 1/2 (0)2
+ 1/4 (2)2 = 2; SD = 1.4
• The expected value is
lower than in the other
example, but the SD
is also lower
probability
return
1/2
2 4 6
What is risk?
Event probability stock
price
Boom 1/4 6
Recession 1/2 2
no change 1/4 4
1/4
B
• The probability density function shows the probability of each alternative outcome
• The tighter the probability distribution of expected returns, the smaller is the total risk
• To judge an investment, one needs to consider return and risk as well; i.e., EV and SD ()
probability
return
1/2
2 4 6
What is risk?
1/4
1/3
B
C
A
21
• Lots of modells in finance assume a bell-shaped probability distribution
• Many variables that are the result of a random process are believed to be best described by a normal distribution. Advantages: – symmetric: probability of negative outcome has the same
weight a a positive outcome. This makes a measure of risk
– if you mix assets with normal distributed returns to a portfolio, the return of the portfolio is normal distributed as well
– Forecasting is much easier if you only need to compute two variables (mean and )
Reward, Risk and volatility
The bean machine
Reward, Risk and volatility
22
• the normal distribution is described by means of two
variables: mean and standard deviation ()
• Deviations from normality:
– Skewness: non-symmetric distribution (measured by cubed deviations from the mean)
– Kurtosis: higher likelihood of extreme values (fat tails), measured by deviations from the mean raised to fourth power
– In theses cases, is not an adequate measure of risk
• Value at risk: if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period
Reward, Risk and volatility
http://www.riskmanagementmonitor.com/the-global-financial-crisis-a-historical-outlier/
Modelling: Normal distribution is not always the norm
By Tracy Alloway (FT)
“It’s these VaR numbers that are really setting this thing off,” goes a line from the film Margin Call, the recent cinematic attempt at turning the financial crisis
into Hollywood drama. While “VaR” may not have been a terribly familiar term for much of Margin Call’s audience, workers in financial markets would have
recognised the reference straight away. “Value at Risk” aims to model how much money a bank or firm is likely to make or lose from trading and was
pinpointed as an important contributor to the global financial crisis.
VaR models failed to forecast the collapse of the US housing market and ensuing crisis; catching off guard banks that relied on them and landing them with
huge, unexpected losses. While the models may live on in the risk management armoury of Wall Street and the wider financial world, they have not survived
unchanged. What is more, a new crop of models and risk management systems – from stress tests to expected shortfall – have sprung up in the three-and-a-half
years since.
“What we have seen is, since the crisis, people are looking to do more than just [basic] VaR,” says Andrew Aziz, who works in the risk analytics business of
IBM. “Prior to the crisis, there was an over-reliance on VaR. It had almost become a silver bullet for measuring risk.” VaR models forecast profit and loss, at a
certain confidence level, based on a bell-shaped, or “normal”, distribution of probabilities. Put simply, that means more moderate gains and losses are predicted
for the vast majority of trading days. A typical interpretation of VaR would forecast a bank to lose more than its VaR – $100m, for instance – once every 10
days on average. The models, first created by a team at JPMorgan in the late 1990s, quickly became a stalwart of risk management for banks and investment
firms, even codified in the Basel banking regulation of the time.
But they turned out to be terrible at interpreting the “tails” of the distributions – or what would happen on trading days that were not inside the main part of the
bell-shaped curve of “normal”, especially when market liquidity disappeared. In 2008, for instance, the profit and loss distribution of Goldman Sachs looked
more like an elongated “U” than the bell shape predicted by VaR. Normal distribution was no longer the norm. The solution since the crisis has largely been to
input numbers that boost the probability of extreme events.
Some banks have also decreased the confidence levels of their VaR models. Others began using “stressed VaR”, which incorporates periods of market turmoil
in its assumptions. David Renz, director of risk advisory at SunGard Financial Systems, a technology company, says: “There has been a trend towards ‘stressed
VaR’ – using stressed calibrations that the regulators ask banks to run.” Indeed, stressed VaR became the favoured model for the Basel committee of banking
regulators, but it has also been criticised. One early Basel study showed trading capital required under stressed VaR was occasionally smaller than under normal
VaR.
“Monte Carlo” models have also become more popular. These generate random values, within a defined range, in an attempt to move away from the normal
distributions of VaR. “We’ve seen more people trying to move to Monte Carlo, because that looks at other distributions,” says Denny Yu, head of risk at
Numerix, which provides risk analytics for banks and buyside firms.
“A lot of work has been going in non-normal distributions,” he adds. But banks and regulators are looking even further afield. Stress tests, as seen in Europe and
the US, have become a regulatory norm. A small industry has also sprung up around “scenario-based” tests, which allow banks and trading companies to
forecast losses based on a particular series of events. “I can run a Monte Carlo for anybody, but it is seen as a random walk,” says Ron D’Vari, chief executive
of NewOak Capital, a consultancy. “The problem is that financial events like these are not random walks.”
For the Basel committee, which is formulating trading book calculations for Basel III, there is also a new model in town.
“Expected shortfall”, like VaR, uses time periods and confidence levels for its forecasts. But it attempts better to capture the “tail” of abnormal events, by
forecasting profits and losses beyond the VaR level. “VaR will give you the cliff but expected shortfall will try to measure the damage beyond the cliff,” says
Mr Aziz. The Basel committee is believed to be considering switching to the newer measure – a decision that would end VaR’s near two-decade reign as the top
regulatory risk management model. But already there is industry grumbling. Like VaR, critics say, expected shortfall does not deal well with market turmoil.
Neither does it address the more fundamental human problem of risk-modelling. Says Mr Renz of Sungard: “Man is exceptionally bad at assuming very low and
very high probabilities.” (http://www.ft.com/intl/cms/s/0/67d05d30-7e88-11e1-b7e7-00144feab49a.html#axzz2aPbo3VJP)
23
• risk-free return on money
market-funds = $1
• Sharpe Ratio: return of
asset minus rate of risk-
free return divided by SD
• Sharpe ratio is
determined by
- rate of risk-free return
- return of the asset
- (volatility)
• The higher the Sharpe
Ratio, the higher the risk-
adjusted return; the better
the investment
Asset A:
EV = 1/3 *6 + 1/3 *2 + 1/3 *4 = 4$
SD: 2.6 1.6$
SR: (4$ - 1$) / 1.68 = 1.78
Asset B:
EV = 1/4 *6 + 1/2 *2 + 1/4 *4 = 3.5$
SD: 2 1.4$
SR: (3.5$ - 1$) / 1.4 = 1.78
Sharpe Ratio
24
• Now say there is another
stock: moneyburn.com
• SD is now 16.3 instead of 1.6
– but is the risk of moneyburn
higher than that of
Rockbottom Tech?
• Idea #4: compute the risk per
unit capital invested; i.e.,
divide SD by EV (coefficient of
variation)
Event probability stock
price
Boom 1/3 60
Recession 1/3 20
no change 1/3 40
EV = 1/3 *60 + 1/3 *20 + 1/3 *40 = 40
#2: 1/3 (-20)2 + 1/3 (0)2 + 1/3 (20)2 = 266
#3: 2.6 16.3
CV: 40 / 16.3 = 2.45
CV A: 4 / 1.6 = 2.5
What is risk?
An example (I)
Rate of return in % for
company under this state
State of
economy
probability TeleCorp Saveway
Boom 0.3 100 20
Normal 0.4 15 15
Recession 0.3 -70 10
Which investment would you prefer and why? Compute
EV, SD and SR (risk-free rate = 3%). Graph the
probability density function.
An example (II)
Rate of return for
Telecorp
State of
economy
probability rate of
return
product
Boom 0.3 100 30
Normal 0.4 15 6
Recession 0.3 -70 -21
EV = 0.3 *100 + 0.4 *15 + 0.3 *(-70) = 15 15
25
An example (III)
Rate of return for
Saveway
State of
economy
probabilty rate of
return
product
Boom 0.3 20 6
Normal 0.4 15 6
Recession 0.3 10 3
EV = 0.3 *20 + 0.4 *15 + 0.3 *10 = 15 15
An example (IV)
SD for Telecorp
State of
economy
return –
EV
(return –
EV)2
(return –
EV)2 * P
Boom 100 – 15 7,225 2,167.5
Normal 15 – 15 0 0
Recession -70 - 15 7,225 2,167.5
SD = 4,335 = 65.84 % 4,335
An example (V)
SD for Saveway
State of
economy
return –
EV
(return –
EV)2
(return –
EV)2 * P
Boom 20 – 15 25 7.5
Normal 15 – 15 0 0
Recession 10 - 15 25 7.5
SD = 15 = 3.8 % 15
26
An example (V)
probability
return 10 15 20
probability
return
0.4
- 70 15 100
0.3
0.4
0.3
expected rate of return expected rate of return
Telecorp Saveway
SR = (15% - 3%) / 65.84 = 0.182 SR = (15% - 3%) / 3.8 = 65.9
Session # 4
Pricing
• Saving means sacrifiying present for future consumption: consumption today is postponed in favor of consumption at some (known or unknown) future point in time
• If you save 100 € today, you want to get compensated for
– the delay of consumption
– the risk of default
– Inflation
• But: how much compensation do you demand?
• Time discounting: computing present values of investment options; making different investments comparable
Why do people save?
27
• Basic idea: one dollar paid next year is less valuable to a dollar received today
• Simplest kind of investment: a simple loan. The lender gives 100 € to the borrower, which promises to give back 110 € in one year
• Simple interest rate is 10€ / 100 € = 0.1 =10 percent
• You receive: 100 € + 100 € x 0.1 = 110; resp. 100 €(1+0.1) = 110
• If you lend 100 for two years, you receive 110 (1+0.1) = 100 € (1+0.1) (1+0.1) = 100 € (1+0.1)2= 121€
• For n years you receive 100€ (1+0.1)n
Discounting
• If you lent 100 €, you will receive 121 € in two years
• Or: 121 € in two years are worth 100 € today
• Time discounting: calculating todays value of dollars received in the future
• Simple loan: 100 €(1+0.1) = 110; resp. 100€ = 110/(1+0.1)
Discounting today year 1 year 2
100 100 100
10 10
1
interest
interest
10 interest
(1+0.1)
(1+0.1)
• Simple loan: 100 € (1+0.1) = 110; resp.
100 € = 110/(1+0.1)
• Discounting 110 €: 110/(1+0.1) = 100
• Discounting 110 € over 2 years: 110/(1+0.1)2 =121
• Generally:
present value = future cash flow / (1+interest rate)n;
with n = number of years
Discounting today year 1 year 2
100 110 121 1/(1+0.1) 1/(1+0.1)
121/1.1 110/1.1
28
• What is the value (price) of a bond with a given interest rate i? Net present value (price)
• What is the yield of a bond, given its face value and its price? Solving equation above for i (yield to maturity)
• A convenient simplification for YTM: current yield
Price and return of a bond
NPV = payment
1+i payment (1+i)2
payment (1+i)n + + + ...
face value (1+i)n +
price = payment
1+i payment (1+i)2
payment (1+i)n + + + ...
face value (1+i)n +
i = coupon price
• Yield to maturity (effective yield) tells you the
effective yield of an investment; i.e. the interest rate
of the loan is 0.1 = 10 %
• Example: you buy a bond for 100, which pays you
back 120 (150) in the next year. Yield to maturity:
Yield to maturity
100 € = 120 € / (1+i)
120 / 100 = 1 + i
1.2 = 1 + i
i = 0.2
100 € = 150 € / (1+i)
150 / 100 = 1 + i
1.5 = 1 + i
i = 0.5
Excel: IVK(value1:value_n); (the formula demands at least one value < 0)
Yield to maturity
• Compare these investments by computing yield to maturity (use Excel): – A: invest 100 €; interest payments 20; repayment 100 at
the end of year 2
– B: invest 1000 €; interest payments 200 €; repayment 1000 at the end of year 4
– C: 10,000 €; interest payments 100; repayment 17,000 at the end of year 3
• A: 20 %
• B: 20 %
• C : 20 %
• Yield to maturity helps to compare different investments with different payout-profiles
29
Yield to maturity
• Compare these bonds by computing yield to maturity (use Excel): – A: price = 100 €; interest payments 20; repayment 100
two years later (plus interest for the second year)
– A: price = 90 €; interest payments 20; repayment 100 two years later (plus interest for the second year)
– A: price = 80 €; interest payments 20; repayment 100 two years later (plus interest for the second year)
• A: 20 %
• B: 27 %
• C : 35 %
• Yield to maturity rises as the price of the bonds decreases; inverse relation between price of a bond and its yield to maturity
• Who gets the stock
– the investor that bids the most money for it
– the investor that takes the best advantage from that stock
– the investor who has the most superior information about that stock
– the investor with the lowest perceived risk
• What determines the price of a stock?
– macroeconomic view: growth expectations, inflation rate, interest rates, exchange rates
– Microeconomic view: dividend forecasts; forecast on the companies future earnings; growth vs. value stocks
– risk and risk attitudes
– liquidity
Price and return of a stock
• Basic idea: compute the value of all future cash flows from the stock by discounting
• Example: you own the stock for one year
• The current value of a stock is the sum of discounted dividends plus the present value of the stock when it is sold
• What if you intend to hold the stock for longer than a year?
Price and return of a stock
Div 1+ir
P1
(1+ir) + current value =
30
• You own the stock for n years
• the one-period-valuation-model can be asily
extended to any number of periods
• If Pn is far in the future, it is difficult to
estimate, but its impact on the value of the
stock decreases
• Generalized dividend model:
Computing the price of a stock
Div1
1+ir
Pn
(1+ir)n + current value = Div2
(1+ir)2 + Divn
(1+ir)n + ... +
Div1
1+ir + current value = Div2
(1+ir)2 + Divn
(1+ir)n = ... + Divt
(1+ir)t t = 1
Computing the price of a stock
• If a firm is not paying dividends or has a very erractic growth
rate, the results of the dividend valuation modell are not
satisfactory
• Price-earnings valuation method: market price per share
divided by annual earnings per share. A high PE means
– that the market expects earnings to rise in future, therefore investors
are willing to pay a higher price
– that the market feels that the companies earnings are very low risk –
this justifies a premium on the stock price
– that the market overestimates the firm‘s future prospects
• Firms in the same industry are expected to have similiar PE-
valuations (peer-group-comparison)
• Problem: definition of earnings? Earnings fluctuate aorun
business cycle; what about expected earnings?
Computing the price of a stock
31
• Other comparative valuation ratios depend on the
kind of stock
• Price-to-book-ratio: price per share divided by book
value of the company per share; value indicator
• Price-to-cash-flow-ratio: cash-flow is less affected
by accounting rules and –decisions
• Price-to-sales-ratio: stock price divided by annual
sales per share. Does not tell you something about
profitability
• Other measures: e.g. price-to-click-ratio – be
creative!
Computing the price of a stock
P/E-ratio for the S&P 500
32
Session # 7
Portfolio
Selection
• Investment / speculation: making money from buying an asset. Risk depends on the type of asset – dividends, interest payments
– price increase of the asset
• Hedging: investing in assets which counteracts the risk of other assets („investment insurance“); risk-reducing strategy.
• Arbitrage: exploiting price differences between markets. Riskless strategy. In perfect markets, there should be no room left for arbitrage
• Diversification: decrease the risk of your portfolio by investing in non-correlated assets
Strategies
The miracle of diversification
Stock A Stock B Portfolio
2002 40 -10 15
2003 -10 40 15
2004 35 -5 15
2005 -5 35 15
2006 15 15 15
av. Ret. 15 15 15
SD 20.2 20.2 0
• Stock A and B have
the same yield and
the same SD
• If you buy either A or
B, your risk will be
20.2
• If you pool both
stocks in one
portfolio, yield
remains the same,
but SD reduces to
zero
• In terms of risk-
adjusted return, the
portfolio is superior to
the single stocks
33
-20
-10
0
10
20
30
40
50
2002 2003 2004 2005 2006
Stock A
Stock B
Portfolio
The miracle of diversification
The miracle of diversification
Stock A Stock B Portfolio
2002 -10 -10 -10
2003 40 40 40
2004 -5 -5 -5
2005 35 35 35
2006 15 15 15
av. Ret. 15 15 15
SD 20.2 20.2 20.2
• Now: Stock A and B
have the same risk-
profile; i.e., if A goes
up, B goes up, too –
and v.v
• Pooling both stocks in
a portfolio now does a
poor job in terms of
diversification
• Pooling assets in a
portfolio only makes
sense if the assets are
negatively correlated;
i.e., if A goes up, B
goes down and v.v
The miracle of diversification
Stock A Stock B Portfolio
2002 40 28 34
2003 -10 20 5
2004 35 41 38
2005 -5 -17 -11
2006 15 3 9
av. Ret. 15 15 15
SD 20.2 20.2 18.4
• Now: Stock A and B
are partially correlated
• Pooling both stocks in
a portfolio now reduces
risk, but not as much
as in the case of
perfectly negative
correlation
• Markowitz (1958): the
risk of a portfolio can
be lower than the risk
of its single assets, as
long as these assets
tend to be uncorrelated
• But how do we
compute correlation?
34
• Correlation:
– negative: if A goes up, B goes down
– positive: if A goes up, B goes up too
• How do we measure „up“ and „down“? By the deviation from
the average, i.e., (xi – E(xi)) respectively (yi – E(yi))
• Idea #1: Multiply (xi – E(xi)) with (yi – E(yi)). If both assets are
positively (negatively) correlated, the product of both terms
will be high (low)
• But: the more data points we have to compare, the higher the
product of both terms
• Idea #2: : divide (xi – E(xi)) * (yi – E(yi)) by the number of data
points; this yields the correlation per data point (Covariance)
How do we compute correlation?
Computing covariance
Stock A Stock B Ai – mean Bi – mean Product
2002 40 -10 25 -25 -625
2003 -10 40 -25 25 -625
2004 35 -5 20 -20 -400
2005 -5 35 -20 20 -400
2006 15 15 0 0 0
Σ 15 15 -2050
CV -410
Excel: KOVAR(Field1:Field2; Field1:Field2)
Stock A Stock B Ai – mean Bi – mean Product
2002 40 28 25 13 325
2003 -10 20 -25 5 -125
2004 35 41 20 26 520
2005 -5 -17 -20 -32 640
2006 15 3 0 -12 0
Σ 15 15 1360
CV 272
Computing covariance
35
• The Covariance yields the mean deviation from the
mean deviation of all products of data points
• But: it does not help to compare different asset
combinations
• Idea #3: divide the mean deviation by the standard
deviation (Correlation coefficient)
• CC = ((xi – E(xi)) / SDx) * ((yi – E(yi)) / SDy)
• Excel: Korrel(FIELD1:FIELD2; FIELD3:FIELD4)
How do we compute correlation?
The correlation coefficient
Stock A Stock B Ai – mean Bi – mean Product
2002 40 -10 25 -25 -625
2003 -10 40 -25 25 -625
2004 35 -5 20 -20 -400
2005 -5 35 -20 20 -400
2006 15 15 0 0 0
Σ 15 15 -2050
SD 20,24 20,24 -410
CC = -410 / (20,24*20,24) = -1
The correlation coefficient
Stock A Stock B Ai – mean Bi – mean Product
2002 -10 -10 25 -25 625
2003 40 40 -25 25 625
2004 -5 -5 20 -20 400
2005 35 35 -20 20 400
2006 15 15 0 0 0
Σ 15 15 2050
SD 20,24 20,24 410
CC = 410 / (20,24*20,24) = 1
36
The correlation coefficient
Stock A Stock B Ai – mean Bi – mean Product
2002 40 28 25 13 325
2003 -10 20 -25 5 -125
2004 35 41 20 26 520
2005 -5 -17 -20 -32 640
2006 15 3 0 -12 0
Σ 15 15 1360
SD 20,24 20,2 272
CC = 272 / (20,24*20,22) = 0.66
• The Correlation coefficient ranges from -1 (perfect negative correlation to +1 (perfect positive correlation)
• If assets are negatively correlated, they serve as a hedge; i.e., if one stock loses, the other one gains (e.g., shares of a producer of suncream and shares of a producer of umbrellas)
• If assets are perfect positively correlated, diversifying by pooling these assets makes no sense
• Diversification means pooling negatively correlated assets
• The more assets, the higher the diversification effect
• But: there is a limit to diversification
How do we compute correlation?
Diversification: Markowitz
Year Stock A Stock B Weight Portfolio
2002 40 28 0,5 34
2003 -10 20 5
2004 35 41 38
2005 -5 -17 -11
2006 15 3 9
Avrg. Ret. 15 15 15
STD DEV 20,2 20,2 18,4
Corr 0,665364902
Year Stock A Stock B Weight Portfolio
2002 28 0,9 29,2
2003 -10 20 17
2004 35 41 40,4
2005 -5 -17 -15,8
2006 15 3 4,2
Avrg. Ret. 15 15 15
STD DEV 20,2 20,2 19,6
37
Year Stock A Stock B Weight Portfolio
2002 28 0,2 37,6
2003 -10 20 -4
2004 35 41 36,2
2005 -5 -17 -7,4
2006 15 3 12,6
Avrg. Ret. 15 15 15
STD DEV 20,2 20,2 19,1
Year Stock A Stock B Weight Portfolio
2002 28 1 28
2003 -10 20 20
2004 35 41 41
2005 -5 -17 -17
2006 15 3 3
Avrg. Ret. 15 15 15
STD DEV 20,2 20,2 20,2
Corr 0,665364902
Diversification: Markowitz
Diversification: Markowitz
Year Stock A Stock B Weight Portfolio
2002 10 0,8 16
2003 -10 20 14
2004 35 41 39,8
2005 -5 5 3
2006 15 -3 0,6
Avrg. Ret. 15 14,6 14,68
STD DEV 20,2 15,2 13,9
Corr 0,306213
Year Stock A Stock B Weight Portfolio
2002 10 0,6 22
2003 -10 20 8
2004 35 41 38,6
2005 -5 5 1
2006 15 -3 4,2
Avrg. Ret. 15 14,6 14,76
STD DEV 20,2 15,2 13,9
Corr 0,306213
• Markowitz: computing a minimum variance-
portfolio by weighting assets according to their
yield, variance and correlation
• There are (efficient) combinations of assets which
bring a higher reward without increasing risk
• So: if you know yield, variance and covariance of
assets, portfolio selection boils down to a simple (?)
computing task – Markowitz-Portfolio
• Problems: market risk, computing a portfolio from
historical data (black swan)
• Has Harry Markowitz a Markowitz-Portfolio?
Markowitz-Portfolios
38
• Can we diversify fom all risk?
• e.g., suncream corp. and umbrella corp.
– your portfolio will not suffer losses due to the weather,
come rain or shine
– what about other reasons for losses, e.g., higher taxes,
recession, inflation, etc.?
– Company-specific risk: lawsuits, strikes, product programs;
events unique to a single firm
• You can hedge company-specific (idiosyncratic) risk,
but not market risk
• Market risk: factors concerning all stocks / assets (=
market portfolio)
Idiosyncratic risk and market risk
-20
-10
0
10
20
30
40
50
10 20 30 1500
# of stocks in portfolio
Portfolio risk
Market risk
Company-specific risk total risk
Idiosyncratic risk and market risk
• It is almost impossible to find uncorrelated stocks; thus even diversified portfolios end up with a market risk
• The tendency of a stock to move with the market is called beta – beta is a measure of the relative volatility of a stock compared to the
market as a whole
– a beta of 1 means that the stock moves exactly as the market does
– a beta of 2 (0.5) means that if the stock market moves up by 10 percent, the stock moves up by 20 (5) percent
• Adding a high (low) beta-stock to a portfolio means increasing (reducing) the portfolio risk
• Beta of a stock measures its contribution to the riskiness of a portfolio
The concept of Beta
39
-20
-10
0
10
20
30
40
50
Idiosyncratic risk and market risk
return of stock
10 20 10 30 40 20 30
return on market
average stock; =1
high- stock
low- stock
• Beta is the market risk, what about superior skills of fund managers to beat the market – alpha?
• Beta = commodity, the market; alpha = skill
• How do you disentangle Beta from alpha?
• Idea: in some markets, nobody is able to beat the market (efficient markets), but some fund managers have superior skill in some (inefficient) markets.
• Result: core-satellite-investing; index-based investment in efficient (core)markets, active management in inefficient (satellite)market
The concept of Alpha
• Definition of risk
– standard deviation
– Sharpe Ratio
• hedging against risk: diversification
– pool non-correlated assets
– measure correlation by correlation coefficient
– but: diversification helps only against idiosyncratic risk
• Beta (= market risk) – relative volatility of a stock compared to the market as a
whole
– Beta of a stock measures its contribution to the riskiness of a portfolio
Risk: a summary
40
Session # 6
Forecasting
• Which techniques are available to forecast security prices? – Technical analysis
– fundamental analysis
– quantitative models
• Is forecasting possible at all?
• If forecasting is possible, it is possible to beat the market, i.e. to be better than the market represented by the average investor or the index
• But if forecasting is not possible what is the alternative?
Forecasting
• Searching for predictable patterns in securities prices
• if there are any reasons for a change in the price and the price will adjust slowly enough, one can identify and exploit a trend during the adjustment period
• i.e. prices respond to a certain group of events / influences always with the same pattern – spot the pattern, exploit the trend
• do security prices have a memory?
• Alternative explanation of certain patterns: data-mining or fooled by randomness
Technical analysis
41
• Attempt to determine the discounted value of a security; if it is larger (smaller) than the market price, the security is under(over)valued; buy undervalued, sell overvalued
• Method: look at all data relevant to the price (interest rates, historic earnings, balance sheet, management, industry, revenues, prospects for the industry, financial statements)
• Idea: find securities which are better than other securities
• Problem: what influences the price of a security? What if all investors use all the data you use?
Fundamental analysis
• Statistical methods: regression (OLS); time-series-analysis, Monte-Carlo-simulation etc.
• E.g. curve fitting: Creating a quantitative model that fits to historic price data; using the model to forecast future prices
• It’s like driving a car by looking through the rear mirror – as long as the road behind you does not make dramatic changes, this might work
• What about the quantity and quality of data?
• Worst case: measurement without theory
Quantitative analysis
Is forecasting possible at all?
42
• Are prices for securities predictable?
• If prices would be predictable, a forecast of a
future price increase would lead to an immediate
jump in prices
• Any information that influences the price of a
security should lead to an immediate jump in the
price
• Thus, if prices jump immediately to a new level as
new information is unveiled, current prices include
all information which is relevant to the stock
• Moreover, as new information is not predictable,
prices of securities are not predictable, too.
Efficient markets
• Efficient market hypothesis:
– weak form: prices reflect all information from the past; i.e.
trend analysis is fruitless; any signal about future
performance is being already exploited
– semistrong form: prices refelct all public available
information regarding the future prospects of the security
– strong form: prices reflect all information relevant to the
security
• if the EM-hypothesis is true, prices follow a random
walk with drift and are not predictable
• prices move only when unexpected information is
being published
Efficient markets
• If prices of securities were predictable, this would be
a proof for market inefficiency, because if one is able
to predict prices, not all information would be already
reflected in the prices
• If you get an additional profit from unveiling new
information, competition for new information will
make markets more efficient
• Degree of efficiency differs across markets: broad,
liquid markets may be close to strong efficiency;
small markets may be not that efficient at all (but if
they deliver superior returns, competition will make
them more efficient)
Efficient markets
43
• If markets are efficient, there are no superior returns
to any strategy applied by other investors – you can
not beat the market
• conclusion: active portfolio management is not able
to outperform the market systematically
• Passive portfolio management: invest in the market,
i.e. the index, additional advantage: lower fees
Efficient markets
44
On October 7, 1998 the Wall Street Journal presented the results
of the 100th dartboard contest. So who won the most contests and
by how much? The pros won 61 of the 100 contests versus the
darts. That’s better than the 50% that would be expected in an
efficient market. On the other hand, the pros losing 39% of the
time to a bunch of darts certainly could be viewed as somewhat of
an embarrassment for the pros. Additionally, the performance of
the pros versus the Dow Jones Industrial Average was less
impressive. The pros barely edged the DJIA by a margin of 51 to
49 contests. In other words, simply investing passively in the Dow,
an investor would have beaten the picks of the pros in roughly
half the contests (that is, without even considering transactions
costs or taxes for taxable investors).
Miller or monkey?
• If security prices drift apart from their fundamental
value for a long time, this would be evidence of non-
efficient markets – capital market anomalies
• Calendar effects: different behaviour of stock
markets on different days of the week, different times
of the month, and different times of year (seasonal
tendencies): Sell in May; Mark Twain-effect,
January-effect
• Behavioral biasses
• One example: Royal Dutch / Shell
Challenging the EMH: anomalies
45
Forecasting: strategic aspects
46
• Some ideas you find in no textbook
• Strategy #1: One of the most efficient strategies - expect what has been yesterday
• Strategy #2: coin a date or a target value – but not both at the same time
• Strategy #3: repeat your forecast again and again – some day you’ll be a guru (“Beck was the only one to forecast Dow 20000”)
• Strategy #4: the mexican sniper – make as much forecasts as possible
• Strategy #5: say what everybody says – that will save your job
Forecasting: strategic aspects
