Investment analysis
Use the slides on blackboard:
Textbook: investments, by bodie kane and marcus (KBM) (11th edition)
-> use it for the assignments (average on 3 assigments = 1/3 grade of the exam)
-> buy book with electroninc learning environment attached to it (see blackboard)
Exam (2/3): written, closed book (questions to see if you understand the content -> not the practical
content of the assignments)
The purpose is to understand the principles, not the mathematics -> focus on economic logic
-> formulas are not that crucial, it’s what’s behind
Use the perspective of an institutional investors (we’re not going to to financial planning -> more focus on
individual investment, hold in account the tax environment)
-> institional: tax environment can be regarderd
TheCityUK: publishes financial reports
What are institutional investors: pension funds, mutual funds, insurance funds
hedge funds: target to wealthy funds etc (not the individuals, advantage: no regulation to sell shares to
individuals)
non-conventional: smaller to conventional
SWF’s: reinvest the proceeds of national ressources (ex: oil industry) -> owns 2% of every stock of the
world
ETF’s: exchange traded funds (kind of mutual fund): difference: mimmicking kind of benchmark
(s&p500’s) (you can buy shares of it: you can trade these etf-shares as normal shares)
-> advantage: very low cost (tiny management fee)
-> cheap way to set up a portfolio of etf’s shares
what is finance about:
-> always combining two dimensions:
time-element (time-value of money)
risk-element (future is uncertain!: you hope that you get you’re money back
o how do we make sure that we only take the risk that is necessary
o the higher the risk, the higher the return (negative interest rate-policy right now in the
banks)
Question: how can we relate risk to award
(not all risks are rewarderd)
Investments = savings (financial assets)
goal: investor becomes consumer
ERR: expected rate of return -> E(r)
risk-free rate: rf
risk premium: E(r)-rf
theoretical concept: every return has some risk attached
1
,Financial assets:
-> ranked according to their risk-level
least risk:
1) cash -> immediately available at your own liking -> you can always withdraw, everywhere
-> commercial paper (relatively risk free), government paper -> T-bills: short-term paper that are issued
on short term: promise an amount on maturity date (discounted paper) (difference = interest rate)
Actua: negative interest rates in Europe (in USA back positive again)
Not completely risk free: also the government can default in it’s obligations
-> in Europe: differences between countries in risk
Europe is trickier than US: us prints it own dollars, in Europe, there is an independant organisation for that
-> but not really risk free: ultimately: you have to exchange your money for consumption (printing money
only inflates the prices: so food becomes more expensive)
We need adjusted risk to inflation
2) fixed income investments -> exactly the same, but on a longer maturity = bonds
-> asset-backed sucrities: for example: the housing prices behind the mortgages
10 year bonds are really risky: because you don’t know the inflation over the course of your investment ->
inflation becomes less predictable over longer maturities
Even the US-government can default sometimes
3) Equity
4) derivatives
-> risky instruments: lot of leverage involved
(We will hardly look at commodities)
Realised returns historically: invested 100 dollars in 1925
T-bills (log-scale): grows to 2052 dollars in 2009
large stocks (US-equity): grows to 215 000 dollars in 2009
-> we see the risk premium to be earned
-> difference = the equity premium
-> return indexes: measures the evolution of an investment (if you reinvest all your profits constantly)
Reward on anual bases: compound rate over 84 years: exercice: g= 9.56% for equity = geometric avarage
rate return
-> risk premium = 6% because g for t-bills is 3%
More quantitave: can we find the differences in rewards on differentend timelines and stocks)
The time value of money
-> discount function (see slides)
-> useful to define asset-pricing
pa = per annum (per year)
6% -> 6 euro coupon every year
after 4 years: you get the 100 euro back so 106 euro
2
, Trading at par: trades at 100
below par: you pay a discounted price: you pay less than 100 to get 100 back in the future
arbitrage strategy: you get a profit, but no risk (doesn’t exist)
most of the time: you observe the inverse discount function: the interest rate function yt
People use interest rates to make comparisons easy
you’re going to invest of certain amount of money: d(t) and you will get 1 at the end
d(t) (1 + yt)t = 1
-> anual rate of return (anualised)`
d(t) = 1 / (1 + yt)t
-> see slides!
term structure of interest rates (crucial concept for bonds)
(cross-sectional comparison)
-> Spot rates = effective rates = yt
In practice: people will use the spot interest rate
<-> quoted interest rates (iQ) : people quote 12% -> it means that you will get of an investment of six
months: half of 12%= 6%
-> it doesn’t work like that for effective interest rates
yt = 12,36% (and not 6%)
this is the effect of compound interest rates
you should always compare effective and not quoted interest rates
-> to go from iQ to yt -> use formula of slide
term structure of interest rates -> to define the asset-prices
-> but there is an arbitrage opportunity: see example
buy 10A: -40 -> 50
sell 4B: +40 -> -48
-> gives 2 profit without investing anything
what if you don’t have B: short-selling (borrow shares from somebody -> but this is rewarderd with a fee)
-> dangerous: if the price goes up, your in trouble
-> hedge funds use this all the time
Some risks are diversifible (if you diversify your portfolio, you don’t feel when one company goes
bankrupt and you lose thagt money you had in shares)
Decide your portfolio strategy
holding-period return (HPR)
RI = 100 (1 + HPR)
-> useful formula to copute returns over some horizons
Also compute the avarage return
gross returns: (1+ R1)(1+R2)…(1+RT)
geometric average: square route of gross returns
(in excel: function GEOMEAN on the 1 + returns series)
3
Use the slides on blackboard:
Textbook: investments, by bodie kane and marcus (KBM) (11th edition)
-> use it for the assignments (average on 3 assigments = 1/3 grade of the exam)
-> buy book with electroninc learning environment attached to it (see blackboard)
Exam (2/3): written, closed book (questions to see if you understand the content -> not the practical
content of the assignments)
The purpose is to understand the principles, not the mathematics -> focus on economic logic
-> formulas are not that crucial, it’s what’s behind
Use the perspective of an institutional investors (we’re not going to to financial planning -> more focus on
individual investment, hold in account the tax environment)
-> institional: tax environment can be regarderd
TheCityUK: publishes financial reports
What are institutional investors: pension funds, mutual funds, insurance funds
hedge funds: target to wealthy funds etc (not the individuals, advantage: no regulation to sell shares to
individuals)
non-conventional: smaller to conventional
SWF’s: reinvest the proceeds of national ressources (ex: oil industry) -> owns 2% of every stock of the
world
ETF’s: exchange traded funds (kind of mutual fund): difference: mimmicking kind of benchmark
(s&p500’s) (you can buy shares of it: you can trade these etf-shares as normal shares)
-> advantage: very low cost (tiny management fee)
-> cheap way to set up a portfolio of etf’s shares
what is finance about:
-> always combining two dimensions:
time-element (time-value of money)
risk-element (future is uncertain!: you hope that you get you’re money back
o how do we make sure that we only take the risk that is necessary
o the higher the risk, the higher the return (negative interest rate-policy right now in the
banks)
Question: how can we relate risk to award
(not all risks are rewarderd)
Investments = savings (financial assets)
goal: investor becomes consumer
ERR: expected rate of return -> E(r)
risk-free rate: rf
risk premium: E(r)-rf
theoretical concept: every return has some risk attached
1
,Financial assets:
-> ranked according to their risk-level
least risk:
1) cash -> immediately available at your own liking -> you can always withdraw, everywhere
-> commercial paper (relatively risk free), government paper -> T-bills: short-term paper that are issued
on short term: promise an amount on maturity date (discounted paper) (difference = interest rate)
Actua: negative interest rates in Europe (in USA back positive again)
Not completely risk free: also the government can default in it’s obligations
-> in Europe: differences between countries in risk
Europe is trickier than US: us prints it own dollars, in Europe, there is an independant organisation for that
-> but not really risk free: ultimately: you have to exchange your money for consumption (printing money
only inflates the prices: so food becomes more expensive)
We need adjusted risk to inflation
2) fixed income investments -> exactly the same, but on a longer maturity = bonds
-> asset-backed sucrities: for example: the housing prices behind the mortgages
10 year bonds are really risky: because you don’t know the inflation over the course of your investment ->
inflation becomes less predictable over longer maturities
Even the US-government can default sometimes
3) Equity
4) derivatives
-> risky instruments: lot of leverage involved
(We will hardly look at commodities)
Realised returns historically: invested 100 dollars in 1925
T-bills (log-scale): grows to 2052 dollars in 2009
large stocks (US-equity): grows to 215 000 dollars in 2009
-> we see the risk premium to be earned
-> difference = the equity premium
-> return indexes: measures the evolution of an investment (if you reinvest all your profits constantly)
Reward on anual bases: compound rate over 84 years: exercice: g= 9.56% for equity = geometric avarage
rate return
-> risk premium = 6% because g for t-bills is 3%
More quantitave: can we find the differences in rewards on differentend timelines and stocks)
The time value of money
-> discount function (see slides)
-> useful to define asset-pricing
pa = per annum (per year)
6% -> 6 euro coupon every year
after 4 years: you get the 100 euro back so 106 euro
2
, Trading at par: trades at 100
below par: you pay a discounted price: you pay less than 100 to get 100 back in the future
arbitrage strategy: you get a profit, but no risk (doesn’t exist)
most of the time: you observe the inverse discount function: the interest rate function yt
People use interest rates to make comparisons easy
you’re going to invest of certain amount of money: d(t) and you will get 1 at the end
d(t) (1 + yt)t = 1
-> anual rate of return (anualised)`
d(t) = 1 / (1 + yt)t
-> see slides!
term structure of interest rates (crucial concept for bonds)
(cross-sectional comparison)
-> Spot rates = effective rates = yt
In practice: people will use the spot interest rate
<-> quoted interest rates (iQ) : people quote 12% -> it means that you will get of an investment of six
months: half of 12%= 6%
-> it doesn’t work like that for effective interest rates
yt = 12,36% (and not 6%)
this is the effect of compound interest rates
you should always compare effective and not quoted interest rates
-> to go from iQ to yt -> use formula of slide
term structure of interest rates -> to define the asset-prices
-> but there is an arbitrage opportunity: see example
buy 10A: -40 -> 50
sell 4B: +40 -> -48
-> gives 2 profit without investing anything
what if you don’t have B: short-selling (borrow shares from somebody -> but this is rewarderd with a fee)
-> dangerous: if the price goes up, your in trouble
-> hedge funds use this all the time
Some risks are diversifible (if you diversify your portfolio, you don’t feel when one company goes
bankrupt and you lose thagt money you had in shares)
Decide your portfolio strategy
holding-period return (HPR)
RI = 100 (1 + HPR)
-> useful formula to copute returns over some horizons
Also compute the avarage return
gross returns: (1+ R1)(1+R2)…(1+RT)
geometric average: square route of gross returns
(in excel: function GEOMEAN on the 1 + returns series)
3
