Beleggingsleer
Section 1: Introduction
Chapter 1: Financial markets, players and instruments
1. What is traded on financial markets
- Investment analysis = The study of how an investment is likely to perform and how suitable it is for
a given investor.
- Financial assets: represent claims on real assets (assets used to produce goods and services)
• Split up in asset classes = groups of investments which share common characteristics, suck as
riskiness and return.
1. Traditional investments = long investments and include the three asset classes stocks,
bonds and cash.
2. Alternative investments = cover a wide range of investments and include commodities
and foreign currencies, derivatives, hedge funds and insurance products, but also
venture capital and private equity, and collectibles.
• Liquidity (and homogeneity) decreases in tendency when moving down the following list:
Classical Investments Alternative Investments
• Bonds • Hedge funds
• Stocks • Managed Futures
• Cash • Currencies
• Derivatives
• Commodities (e.g. gold!)
• Private equity
• Gems and stones
• Fine art, wine…
- Assets:
1. Bonds/fixed income = securities that are issued by a firm or government for a specific term (=
maturity). They provide periodic payments (=coupon) from the issuer to the holder of the
security.
• Maturity: +/- 4-10y
• Positive: all cash flows are known in advance + risk is restricted to the default risk
▪ Plain vanilla bond/note: Bond with standard structure
▪ Zero Coupon Bond: Bond without any coupon payment
▪ Floating rate notes (FRN): The interest rate depends on a reference rate,
such as LIBOR or EURIBOR; reverse/inverse floater (as example of a bull FRN)
▪ Inflation-Protected Bonds: have become increasingly popular
▪ Structured note: a bond (note) issued with some unusual clause, often
something option-like. For example the yield will be enhanced if event X
occurs.
▪ Mortgages and Mortgage-Backed Securities
, 2. Money market securities/cash
• Money market securities/cash = securities with a maturity when issued of not more
than one year, sold by governments, financial institutions and corporates.
! It’s a segment of the fixes-income market
o Treasury bills: Short-term US government bonds (up to one year), highly
liquid, more or less riskless, sold with discount
o Commercial Paper: Money market securities issued by banks or companies
o Certificates of deposits: Short-term money market security, issued by a
bank, usually higher interest rate than deposit (as they cannot be withdrawn)
o Bankers Acceptances: A security that is drawn on a bank and – after
acceptance – can be traded on markets
o Eurodollars: deposits in USD, but outside the US
o Repurchase Agreements (RPs): Repos, sale and repurchase agreements
3. Equity
• Equity = represents an ownership claim on the earnings and assets of a firm. It’s a
residual claim, unlimited maturity and limited liability.
• Common/preferred stock.
4. Currencies
5. Derivatives: the value is derives from the underlying asset’s value (ex. Futures and options)
6. Commodities
2. Where financial assets are traded
- Financial assets: mostly traded on financial markets.
• Past: Fairs = provided periodic meeting places for traders, who mainly dealt in real goods, but
also in currencies and money.
• Then: Permanent exchanges or bourses = meetings that took place at the houses of rich
families -> ‘bursa’.
o Private Bourses: Founded by private individuals and entities for the purpose of
security trading. (Private does not mean without regulation!)
o Public Bourses: Origin in Emperor Napoleon I. Public institution with brokers
appointed by government and monopoly over transactions. Most moved to private
bourses.
o Bankers’ Bourses: Banks as the major or only traders in securities. Regulation of the
banks and the markets. Most of them moved to private bourses.
• Now: Private bourses are nowadays dominating.
- Players:
1. Investor: seek to boost their savings on the markets.
2. Broker: act as agent for investors, set prices and perform the deals. They trade on the
account of others and they live from the fees received.
3. Dealers: trade on his own account and seeks to profit from these trades.
4. Agents: banks and other institutional investors, such as pension funds, mutual and hedge
funds.
5. Central banks: act on financial markets, by providing or absorbing liquidity, governing
interest rates and directly intervening mainly on the foreign exchange market.
,- Execution system
1. Price-driven/quote-driven/dealer market: highly liquid + order execution is guaranteed.
2. Order driven market: more transparent.
Chapter 2: Risk and return
- The return = the ratio of money gained or lost on an investment relative to the amount of money
invested.
• The holding period return over the period from t=0 to t=Y: HPRt = PT/Pt-1 or HPRt = 100/Pt-1
o P0 = initial investment/ price at t=0; Pt= final payout/price at t=T.
o Good measure only if the holding period is the same for all assets under
consideration.
• Annual percentage rate/ average percentage rate:
o APR = HPR/T
o Does not consider any reinvestments or payouts.
• Effective annual rate: EAR = (HPR + 1)1/T – 1.
o => relation: APR = [(1+EAR)T -1]/T
- Work with logarithmic instead of percentage returns: rt = ln(Pt/Pt-1) = ln(Pt) – ln(Pt-1).
Advantages:
• We cab easily aggregate returns to lower frequencies just by summarizing the high frequency
returns.
• It gives the initial price after a price increase followed by a decrease.
• The return in price quotation and indirect quotation only differ by sign, but not in magnitude.
- Sample variance:
2= 1 n
n s =1
r(s)−r 2
• R--= mean variance
• standard deviation = sqrt(σ2)
1
- The unconditional return: 𝐸(𝑟) = ∑𝑛𝑠=1 𝑝(𝑠)𝑟(𝑠) = 𝑛 ∑𝑛𝑠=1 𝑟(𝑠)
• = the average of the conditional expectations, weighted by the scenario probabilities.
• p(s) = probability of state s and r(s) = the (conditional) expected return in state s.
- The Sharpe ratio: Risk premium/SD of the excess return.
• Sharpe ratio = the price of risk, or reward to variability
• Negative: only for an investor’s whole portfolio + only considers risk in terms of the standard
deviation.
Chapter 3. Distributional Properties of Financial Market Series
1. Some stylized facts
- Moments of distributions:
1. First moment: the mean
2. Second moment: the variance
, 1
∑ (𝑟 −𝑟̄ )3
𝑁 𝑡 𝑡
3. Third moment: The sample skewness: 𝑆= 3
1 2
( ∑𝑡(𝑟𝑡 −𝑟̄ ) )2
𝑁
• Skewness provides info about a distributions symmetry.
o 0: symmetric distribution
o >0: right-skewed
o <0: left-skewed
1
∑ (𝑟 −𝑟̄ )4
𝑁 𝑡 𝑡
4. Fourth moment: the (excess) kurtosis: 𝐾 = 1 2 2
−3
( ∑𝑡(𝑟𝑡 −𝑟̄ ) )
𝑁
• High kurtosis: means more of the variance is the result of infrequent extreme deviations
o >0: leptokurtic
o <0: platykurtic
2. Measuring historical volatility
- Volatility is important for
1. Investment decisions
2. Performance evaluation
3. Risk management
- There are two ways to get a volatility forecast:
1. Implied volatility = the volatility that is consistent with observed option prices.
2. Historical volatility = use historical price series as a tool to forecast future volatility
- Unfortunately volatility is a latent factor, therefore we need an estimator. But there is no unique
way to estimate it => we have to make decisions:
1. Sample length: How far do we look back?
2. Sample frequency: How frequently do we collect/use data?
3. Measure to use: Which assumptions on the price process?
1. The sampling lenght
- Long sample => rather measures the long term average volatility
Short sample => introduces estimation errors and puts too much weight on the very recent past
- A reasonable choice is to use a sample of the same length as the forecast horizon
-> specifically for share prices: use multiples of three months (=> constant number of
quarterly reporting periods or macro announcements)
2. The sampling frequency
- Daily data: ~5 times as many observations compared to weekly data
Weekly/monthly data: less impact of holidays, particularly if several markets analyzed
-> Rule of thumb: weekly data rather for longer forecasting horizons and several
markets, daily data else
3. The choice of the volatility measure: price ranges
Section 1: Introduction
Chapter 1: Financial markets, players and instruments
1. What is traded on financial markets
- Investment analysis = The study of how an investment is likely to perform and how suitable it is for
a given investor.
- Financial assets: represent claims on real assets (assets used to produce goods and services)
• Split up in asset classes = groups of investments which share common characteristics, suck as
riskiness and return.
1. Traditional investments = long investments and include the three asset classes stocks,
bonds and cash.
2. Alternative investments = cover a wide range of investments and include commodities
and foreign currencies, derivatives, hedge funds and insurance products, but also
venture capital and private equity, and collectibles.
• Liquidity (and homogeneity) decreases in tendency when moving down the following list:
Classical Investments Alternative Investments
• Bonds • Hedge funds
• Stocks • Managed Futures
• Cash • Currencies
• Derivatives
• Commodities (e.g. gold!)
• Private equity
• Gems and stones
• Fine art, wine…
- Assets:
1. Bonds/fixed income = securities that are issued by a firm or government for a specific term (=
maturity). They provide periodic payments (=coupon) from the issuer to the holder of the
security.
• Maturity: +/- 4-10y
• Positive: all cash flows are known in advance + risk is restricted to the default risk
▪ Plain vanilla bond/note: Bond with standard structure
▪ Zero Coupon Bond: Bond without any coupon payment
▪ Floating rate notes (FRN): The interest rate depends on a reference rate,
such as LIBOR or EURIBOR; reverse/inverse floater (as example of a bull FRN)
▪ Inflation-Protected Bonds: have become increasingly popular
▪ Structured note: a bond (note) issued with some unusual clause, often
something option-like. For example the yield will be enhanced if event X
occurs.
▪ Mortgages and Mortgage-Backed Securities
, 2. Money market securities/cash
• Money market securities/cash = securities with a maturity when issued of not more
than one year, sold by governments, financial institutions and corporates.
! It’s a segment of the fixes-income market
o Treasury bills: Short-term US government bonds (up to one year), highly
liquid, more or less riskless, sold with discount
o Commercial Paper: Money market securities issued by banks or companies
o Certificates of deposits: Short-term money market security, issued by a
bank, usually higher interest rate than deposit (as they cannot be withdrawn)
o Bankers Acceptances: A security that is drawn on a bank and – after
acceptance – can be traded on markets
o Eurodollars: deposits in USD, but outside the US
o Repurchase Agreements (RPs): Repos, sale and repurchase agreements
3. Equity
• Equity = represents an ownership claim on the earnings and assets of a firm. It’s a
residual claim, unlimited maturity and limited liability.
• Common/preferred stock.
4. Currencies
5. Derivatives: the value is derives from the underlying asset’s value (ex. Futures and options)
6. Commodities
2. Where financial assets are traded
- Financial assets: mostly traded on financial markets.
• Past: Fairs = provided periodic meeting places for traders, who mainly dealt in real goods, but
also in currencies and money.
• Then: Permanent exchanges or bourses = meetings that took place at the houses of rich
families -> ‘bursa’.
o Private Bourses: Founded by private individuals and entities for the purpose of
security trading. (Private does not mean without regulation!)
o Public Bourses: Origin in Emperor Napoleon I. Public institution with brokers
appointed by government and monopoly over transactions. Most moved to private
bourses.
o Bankers’ Bourses: Banks as the major or only traders in securities. Regulation of the
banks and the markets. Most of them moved to private bourses.
• Now: Private bourses are nowadays dominating.
- Players:
1. Investor: seek to boost their savings on the markets.
2. Broker: act as agent for investors, set prices and perform the deals. They trade on the
account of others and they live from the fees received.
3. Dealers: trade on his own account and seeks to profit from these trades.
4. Agents: banks and other institutional investors, such as pension funds, mutual and hedge
funds.
5. Central banks: act on financial markets, by providing or absorbing liquidity, governing
interest rates and directly intervening mainly on the foreign exchange market.
,- Execution system
1. Price-driven/quote-driven/dealer market: highly liquid + order execution is guaranteed.
2. Order driven market: more transparent.
Chapter 2: Risk and return
- The return = the ratio of money gained or lost on an investment relative to the amount of money
invested.
• The holding period return over the period from t=0 to t=Y: HPRt = PT/Pt-1 or HPRt = 100/Pt-1
o P0 = initial investment/ price at t=0; Pt= final payout/price at t=T.
o Good measure only if the holding period is the same for all assets under
consideration.
• Annual percentage rate/ average percentage rate:
o APR = HPR/T
o Does not consider any reinvestments or payouts.
• Effective annual rate: EAR = (HPR + 1)1/T – 1.
o => relation: APR = [(1+EAR)T -1]/T
- Work with logarithmic instead of percentage returns: rt = ln(Pt/Pt-1) = ln(Pt) – ln(Pt-1).
Advantages:
• We cab easily aggregate returns to lower frequencies just by summarizing the high frequency
returns.
• It gives the initial price after a price increase followed by a decrease.
• The return in price quotation and indirect quotation only differ by sign, but not in magnitude.
- Sample variance:
2= 1 n
n s =1
r(s)−r 2
• R--= mean variance
• standard deviation = sqrt(σ2)
1
- The unconditional return: 𝐸(𝑟) = ∑𝑛𝑠=1 𝑝(𝑠)𝑟(𝑠) = 𝑛 ∑𝑛𝑠=1 𝑟(𝑠)
• = the average of the conditional expectations, weighted by the scenario probabilities.
• p(s) = probability of state s and r(s) = the (conditional) expected return in state s.
- The Sharpe ratio: Risk premium/SD of the excess return.
• Sharpe ratio = the price of risk, or reward to variability
• Negative: only for an investor’s whole portfolio + only considers risk in terms of the standard
deviation.
Chapter 3. Distributional Properties of Financial Market Series
1. Some stylized facts
- Moments of distributions:
1. First moment: the mean
2. Second moment: the variance
, 1
∑ (𝑟 −𝑟̄ )3
𝑁 𝑡 𝑡
3. Third moment: The sample skewness: 𝑆= 3
1 2
( ∑𝑡(𝑟𝑡 −𝑟̄ ) )2
𝑁
• Skewness provides info about a distributions symmetry.
o 0: symmetric distribution
o >0: right-skewed
o <0: left-skewed
1
∑ (𝑟 −𝑟̄ )4
𝑁 𝑡 𝑡
4. Fourth moment: the (excess) kurtosis: 𝐾 = 1 2 2
−3
( ∑𝑡(𝑟𝑡 −𝑟̄ ) )
𝑁
• High kurtosis: means more of the variance is the result of infrequent extreme deviations
o >0: leptokurtic
o <0: platykurtic
2. Measuring historical volatility
- Volatility is important for
1. Investment decisions
2. Performance evaluation
3. Risk management
- There are two ways to get a volatility forecast:
1. Implied volatility = the volatility that is consistent with observed option prices.
2. Historical volatility = use historical price series as a tool to forecast future volatility
- Unfortunately volatility is a latent factor, therefore we need an estimator. But there is no unique
way to estimate it => we have to make decisions:
1. Sample length: How far do we look back?
2. Sample frequency: How frequently do we collect/use data?
3. Measure to use: Which assumptions on the price process?
1. The sampling lenght
- Long sample => rather measures the long term average volatility
Short sample => introduces estimation errors and puts too much weight on the very recent past
- A reasonable choice is to use a sample of the same length as the forecast horizon
-> specifically for share prices: use multiples of three months (=> constant number of
quarterly reporting periods or macro announcements)
2. The sampling frequency
- Daily data: ~5 times as many observations compared to weekly data
Weekly/monthly data: less impact of holidays, particularly if several markets analyzed
-> Rule of thumb: weekly data rather for longer forecasting horizons and several
markets, daily data else
3. The choice of the volatility measure: price ranges
