Investments
Practicalities
Why should you take this course?
- Value practical implementations, not a theory course, use the theory, valuable later in the
career
- Slide: questions that we will answer
Course overview: 4 parts
- 1. Introduction
- 2. Portfolio theory: active vs. passive investing
- 3. Fixed income investing
- 4. Applied portfolio management (also guest lecture here)
You will enjoy this course if…
- Risk and uncertainty is key in investments, that is why it is hard
- Not mathematical, but some basic calculations are necessary
- About the application, not the theory
- A lot of terms we already know will be thought
Activities
- Every week one topic
- Learn by doing: participate in class
- Discussion forum on Toledo
o Structure, per topic, about lecture material or about exercises
Lecture material
- Handbook investments, bodie, kane, Marcus (13th edition) -> buy it
Lecture material
- For each topic: the slides
- Solutions to the exercises that you need to be able to solve will be on toledo
o If the solution is not there, we don’t have to know the exercise
- Some extra literature
- Excel files with solution
- Video clips
- New material: available Friday 1pm
- Recordings of the lectures (always available)
Evaluation
- Januari: exam (80%) + group assignment (20%)
- Assignment: 2 or 3 students per group (specific or random team)
o REGISTER FOR A TEAM!!!!
o DEADLINES
o Assignment will be posted by the end of October
o She will help, but only if you come as a team to her, sometimes she will even give
part of the solution, important to work as a team
o Excel assignment -> you need to be good at excel for finance jobs
- Exam January: theory and exercises
- Exam September: assignment does not count anymore
1
, o Except for students that do not participate the January exam because of overlap, and
do the exam in September
- !! Most exam questions come from the handbook (80% of the questions)
o This says you the level that you need to know
Investments: capital markets and products
= an introductory topic to give you the broad context of the class
If we talk about investments, we talk about capital markets, we talk about the products that are
traded within these markets
On the slides: chapters in the BKM that you need to know!
Background reading: not compulsory, only if you want to know more about this topic
Financial markets
The class is about investments in financial instruments, financial products
Function
Why do these financial products exist? Multiple functions of investments of financial markets
1. Share/transfer risks
- It might be that you are exposed to a financial risk, but you are not willing or unable to take
this risk, then a financial product allows you to transfer that risk
- In practice: Most people tend to overestimate their risk bearing capacity. Most people think
that they like risk, that they can bear the risk; that their risk aversion is low; however in
reality, this is not the case. People take on risk, assuming that they can bare the risk, and
when the risk materializes, they panic. Panic is the worst environment to take decisions, the
worst decisions are made in a period of stress
- This is why it is important to understand your risk appetite
- How does it come that people tend to overestimate their risk bearing capacity?
o 1. Biases
▪ Behavioural finance, we do observe some difference in risk taking behaviour
vb. male vs. female
o 2. People are a bit blind for risk. There is a trade off between expected return and
risk, one thing does not come without the other. People tend to ignore the risk
component and are extremely focussed on the return component.
▪ Of course I prefer more return, but then they forget about the fact that more
return = more risk
▪ Overly focussed on the return, and forget the risk
o 3. Hard to understand what risk is
▪ What is risk? Two key concepts
▪ The fact that there are multiple outcomes -> no certainty, but probabilities;
you don’t know ex ante which outcome will materialize
▪ At least one of the outcomes is harmful.
• BUT being less than expected is not necessarily harmful
• Suppose: someone gives me 100, 200 or 300 euros, all with different
probabilities. I have an expected return (150), I could end up with
less than I expected => does not mean it is a risk; because all of the 3
scenario’s are good scenario’s
▪ Intuitive definition in normal situations: Risk is really about the likelihood
that something bad/harmful can happen to you -> this is not the definition of
risk in finance
▪ Definition in finance of risk:
2
, • We use volatility in the definition of risk. How does volatility fit in
that more intuitive definition of risk? Not straightforward, you need
statistical knowledge to do that. Many investors do not have that
knowledge, or they have the knowledge but they do not necessarily
make the translation.
• What does she mean by that? If you think about probabilities of
different outcomes and one of the outcomes being negative/harmful
-> this means that you end op with a description that is more
broader than just volatility
• Expected return is the first moment. Volatility is ultimately the
second moment of your distribution
• But the intuitive definition is more about the whole distribution.
Why do we typically work with expected return and volatilities?
Because we assume normal distributions. And we have normal
distributions the first two moments define our distribution. But if
you just limit yourself to these two moments, you might forget what
it really means in terms of the different outcomes that can happen
to you and the likelihood of these outcomes. But it is still there.
• Simple example about this
Vb. we have an investment, vb. you buy a stock
- Typical expected return on an annual basis
o ! always work on an annual basis, if an expected return of volatility is not annualized,
annualize it, because you typically have intuition for annual numbers
- What would be a typical expected return and volatiltiy on a single stock investment?
o E(R) = 13% = expected return on an annual basis
o σ(R) = 33% = volatility on an annual basis (not of a diversified portfolio, but on a
single investment)
- What does that mean if you invest in this asset? Lets impose a normal distribution
- Tekening
o So this is probably much more informative than just looking at the expected returns
and volatilities to understand whether your able to bear a particular amount of riks
o Now you know that If you take on this investment, it means that you have a 16%
chance to end up with a return lower than -20%
o Once you impose a distribution and you look at the probabilities associated with the
different outcomes, it becomes much more easy to grasp whether you are able to
bear the risk
o ! in reality returns are not normally distributed, it is worse, because there is more
mass in the tails (extreme negative or extreme positive returns)
▪ Being skewed is not necessarily bad, only if it is to the left (more negative
probabilities)
3
,VERDER: why do these products exist
2. Financial markets allow to separate the timing of income (when you get the income) and
consumption (when you want to consume the income): store wealth to transfer to the future
o Financial products allow you to make an advance on future income
o Vb. taking out a loan or obligation
o If you buy a bond, you transfer your storewealth to the future
o Transferring wealth over time allows you to smooth consumption (no peaks and
valleys in the consumption pattern)
3. Financial markets allow to separate ownership and management in support of large-scale
businesses (but be careful with associated agency problems)
o Without financial markets, companies would not be able to grow as much as they do
today.
o A firm might not have sufficient means to take the next step in their growth process,
because they don’t have the funding that they need. Financial markets can help
them secure that funding to grow
4. Financial markets allow to allocate resources efficiently i.e. to most productive real
investments (= informational role of financial markets)
o Efficiency of a market
o Which crucially depends upon the degree of efficiency
o Market efficiency: markets are efficient if all relevant information is reflected in
prices
o Often when we think about market efficiency, we immediately think about arbitrage
opportunities; if a market is not efficient, there are arbitrage opportunities
o But the degree of market efficiency is much more important than trading
opportunities, whether you can re… arbitrage profits; it all has to do with an
allocation of resources -> if the market is not efficient, too few money goes to
particular investments, and too much money to others -> only when the market is
efficient, the different opportunities get the money that they deserve
o Market efficiency is really important -> not just for the investors or for arbitrage, but
for the economy to grow in a sustainable way
Asset classes
If you think about the different products/instruments that are traded/that exist, there exists a large
range of products.
In this opleidingsonderdeel, we will limit to very standard products, mainly two big asset classes
- Money market instruments
o = short term debt security with low risk
o She will talk about it as ‘the risk free’
o Some are actually riskier than others within this class, but as compared to other
assets in the economy, they are the risk free instruments
o Vb. cash, products that allow you to save
- Capital market instruments
o Here we typically have longer term instruments, could be debt (bonds ) and equity
(stocks)
o When prof refers to investing, she means this
Each instrument is unique in terms of (un-)certainty of payments (how likely the payments are) and
timing of payments (when you can receive the payements) and has a distinct contribution to the
investment portfolio
- Unique risk return profile
- This makes that the different instruments all have a different role to play in a portfolio
4
, - This is why, when we think of a diversified portfolio, consists of stock AND bond
1. Money making instruments
List of the instruments that you can regard as a money making instrument:
- Treasury bill (T-bill): government debt obligation with a maturity < 1 year
o Short term debt, issued by the government
- Certificate of deposit (CD): time deposit at a bank
- Commercial paper (CP): short term unsecured debt issued by a large corporation
o You need to have good credit quality, to be able to issue this CP
- Bankers’ acceptance: a bank promise to pay a prespecified amount
- Repurchase agreement (repo or RP) and reverse repo: a short term loan (usually overnight)
using other securities (usually government securities) as collateral
o Repo could also be seen as a spot sale of securities combined with a forward
purchase of securities
- Interbank loans: short term loans among banks (from which reference rates are being
calculated e.g. ESTR, EURIBOR)
o Loans in between banks, wholesale market, interbank market
o ESTR rate = overnight rate in euros
▪ Libor scandal 2014 -> change in reference rates -> so ESTR rats is a new rate
▪ Before? Bank were being asked: at what rate would you be willing to lend to
someone else
▪ What is new in the ESTR rate? Effective rate, average rate that was charged
to one another
o EURIBOR = can go from one week up to one year
- Central bank deposits and loans: short term deposit/loan of a bank by its central bank
o Internet: The main refinancing operations rate is the interest rate banks pay when
they borrow money from the ECB for one week
o Risk free, not for retail investor, but for institutional investors
o Central bank deposits an loans; deposits for the loans that banks/fin institutions do
with the central bank
▪ Vb. Central bank in USA -> federal funds
▪ Vb. for Europe (ECB) -> MRO (main refinancing operations)
▪ Vb. deposit facilities, lending facilities (short term = one week), MRR
(marginal reserve requirements)
o It are these policy rates that used to be negative for a while
▪ When banks deposited money at the ECB, they needed to pay for this
(negative rates)
▪ Nowadays sinds 2022 it is back to zero, and now it is positive again
- Call loans: loans that need to be repaid, on demand at any time; often made by banks to
brokerage firms to fund individuals that buy on margin
o Brokerage firm (internet): fin instelling die als tussenpersoon optreedt bij het kopen
en verkopen van beleggingen. Deze bedrijven bieden investeerers toegang tot fin
market en kunnen handelstransacties namens hun klanten uitvoeren
o To buy on margin (internet): geld lenen van een broker om een belegging te doen;
het onderpand vanhet geleende bedrag zijn de beleggingen. Je kan dus meer
investeren dan je hebt omdat je kan lenen (zie verder)
o Clients that want to leverage their portfolio, need to take out a loan. The brokerage
firm gives the loan, but actually the brokerage firm takes out a loan at a bank = call
loan
- Savings deposit
5
,Most money market instruments are low risk, but they are not risk-free!
- They are not all equally risk free
- When all things go well, the difference in risk between them is small; but in times of stress,
spreads will increase
- In general T-bills (government bond) have lowest risk, both in terms of credit risk, as well as
liquidity risk
Figure about the spread between the different rates
- TED Spread = difference between the T-bill and the LIBOR rate
- Both move quite equally but in moments of crisis, the spread increases drastically
- Vb. financial crisis 2008 & covid 2020, TED Spread spiked -> higher liquidity and credit risk of
the LIBOR rate
2.1 Capital market instruments: bonds (debt)
Key concepts here:
- Longer term debt instruments with wide range of maturities
o It can be 1 year, but also 10, 20, 30… years
- Various credit qualities: from high credit-quality instruments to (very) low credit-quality
(junk) instruments
o Different bonds: bonds with high credit quality (vb. investment grade bonds), bonds
with low credit quality (junk bonds)
o When you make an investment, you need to check the credit quality
o If they offer you high coupons, then you know that the credit quality will be poor;
you need to be offered high returns, high yields, otherwise you won’t buy that
instrument
- Liquidity varies from very high to almost zero
o Some bonds are very liquid vb. government bonds
o Some bonds can be very poor, low -> extra risk -> if you want to step out, you might
have a hard time finding a counterparty or you will only be able to sell off the bond
at a discount
6
, - Often in smaller denominations such that they can be held by retail investors
o It is because of the small denominations that the instruments are also attractive to a
retail audience
- Often not traded on the exchange, but rather traded over the counter (OTC) via dealers
- Expressed as a % of the par value
o Par value = nominal value
o Then we don’t have to refer to the denomination. You can get a good grasp of what
the price really is (cheap or expensive)
o Vb. it you say ‘the bond is traded at 95%’, you know that it trades at 95% of its par
value
- Typically pay coupon interest (annual or semi-annual)
o Bonds pay coupon interest, on an annual or semi-annual basis
o Vb. if we have a bond that pays out coupon at 6% -> at one point in time you receive
6% of the nominal value as a coupon. If the 6% is on a semi-annual basis, every 6%
you get 3%
- Performance measurement: hpr or yield with (including a risk premium for credit risk)
o When you want to measure the performance of a bond, we will see in this class
numerous ways to calculate the return. It depends on the instrument, and what the
kind of metric is you are looking for.
o It could be a holding period return, vb. the return that you earn when you buy the
bond today and sell it off tomorrow
o It could be some kind of yield concept. A yield = internal rate of return;
▪ vb. Yield to maturity = assumes that you hold on to the bond up until
maturity
▪ vb. yield to call, if you have a callable bond
▪ vb. current yield
o we will see which concept is used in which circumstances. Because for some bonds,
talking about yield to maturity doesn’t make sense and you need another concept
vb. yield to call
different kinds of bonds, depending upon the identity of the issuer
- Treasury notes: government debt with 1 yr < maturity < 10 yrs
o Up until 10 years
- Treasury bonds: government debt with maturity > 10 yrs
o More then 10 years
o But you can refer to all of them as a bond (also the notes)
- Treasury inflation-protected securities (TIPS): government debt with principal and interest
adjusted for inflation
- Federal agency/municipal bonds: debt issued or guaranteed by, respectively, a federal
agency, state or local government
- Corporate bonds: debt issued by a large corporation; typically larger default risk as compared
to government debt; options included (callable, convertible)
- Asset backed debt: proportional ownership claim in a asset pool (cf securitization)
o This gives u some ownership
o Not one particular issuer, but a pool of assets
2.2 Capital market instruments: stocks (equity)
Stocks (common shares) are issued by corporations and represent ownership in a firm (stock gives
you ownership in a firm)
- share the distribution of profits
7
, - have voting power at shareholders’ meeting (this makes it different from a bond, a bond only
has financial returns)
Equity represents a residual claim: you only receive payout if all other claims (e.g. salaries, debt,
taxes) are paid (the last one to be paid)
- Because of the residual claim, equity is more risky than bonds
- At the end of the pecking order
Equity has limited liability: minimum share price is zero (return is bounded at -100%)
- Limited liability: If the firm goes bankrupt, even tough you are a shareholder, you are not
liable with your own wealth (you can loose it al but not more than you put in yourself)
- This is important legally, but also for finance theory or modelling this is important. The fact
that equity has limited liability, says something about which distribution is appropriate.
o Earlier we assumed the normal distribution of the returns
o Is this in line with limited liability? No, because you cannot go in the minus and the
rang of a normal distribution is [-infinity, + infinity] -> prices can go negative
o So the normal distribution is not appropriate to talk about returns for shareholders
o How do we solve this? Sometimes we just work with a normal distribution and ignore
this fact, because it is true that the likelihood of ending deep in the negative tail is
small. But sometimes we do solves this -> two things that we could do when
modelling returns and we want to work with the normal distribution
▪ 1. We use log-returns -> you cannot take a log of a negative number, so by
definition, the prices cannot go below zero
▪ 2. What is the frequency of the returns? Daily returns -> then you naturally
put boundaries on the distribution, because the likelihood that on a daily
basis your return is less than 100% becomes extremely small
• Whether you calculate a daily return or a daily log return, the
numbers are approximately the same
• But if you lengthen your horizon: an annual return and an annual log
return -> those numbers are not the same
• Only use log returns when you work on a daily basis, when the
frequency is high
o => this is how we can incorporate the limited liability in finance theory
Performance measurement: return (mostly reward for market risk)
- We will calculate returns, just the difference in prices
Note: preferred shares are related and possess common equity features, but also bond features
(combination of bond and equity):
- share of ownership (like stocks)
- no voting power (like bond)
- promise of fixed dividend (often cumulative) (like bond)
Investment funds
Having introduced the basic financial instruments, many retail investors and even also institutional
investors will not necessarily trade individual instruments. They will trade funds, they invest in a fund
(whatever the underlying structure is).
People often invest in a pool, this allows them to profit from economies of scale
- They then have ownership in this pool of assets
8
,Benefits
- Diversification and divisibility
o As a part of this larger pool, you can more easily diversificate. Because the amount
that you have can be small, but in a pool, you can diversificate
o Divisibility = deelbaarheid
- Lower transaction costs
o Entering a fund is costly, but within the fund the transaction costs will be lower,
because they will be able to trade at more beneficial …spreads as compared to you
- Professional management
o They have tools at their disposal to manage this portfolio in professional in a timely
fashion
- Record keeping and administration
o This is mainly important in foreign investments
Net asset value
= important concept in funds
Gives you an idea of what a share in the fund is worth. It is the
- (market value of assets – liabilities) / shares outstanding
- If the NAV increases, your investment becomes worth more
When the composition of the fund is changed (when they buy/sell), this leads to a turnover
- Keep track of the turnover of the fund as an investor, because turnover generates
transaction costs. If the fund turns over a lot, it might eat up your return
- Different turnover rate, depending upon the investment strategy. If you have the two big
classes:
o Passive investment -> very low turnover, low transaction costs
o Active investment -> turnover can be a lot, high transaction costs
o Behavioural biases -> male managers turn over more than female managers doe
o If you turnover because there are good investment opportunities, that is fine, but if
you turnover just because of the fun of being active and making investment
decisions, this will be expensive for the ultimate investors/owners
- Turnover rate = market value of asset sold / market value of assets
Investment companies
Now if we talk about the fund, there are many different structures.
1. Open-end fund (’mutual fund’): managed fund with specified investment policy that issues new
shares when investors buy in and redeem shares when investors cash out; they are priced at NAV
(traded at day-end only)
- Most of the time, when someone talks about a fund, it is about a mutual fund
- The number of outstanding share changes upon demand. If there are more investors that
want to step in, new shares are being created. If more investors want to step out, shares are
being redeemed
o So the number of shares outstanding is not fixed, but varies with the interest in the
fund
- This makes that the open end funds, they trade at NAV -> when you want to step in, you pay
the nav, really what it is worth
o But you will not be able to trade them intra day, you will not be able to buy them in
the market, you buy the immediately from the fund
o This means when you want to place an order in the fund, you do not know at which
price you will be able to buy, because the nav is only calculated at the end of the day,
and then everyone who wants to step in/out will trade at that nav
9
, - => you cannot trade quickly, you cannot trade intra day and you do not know in advance
when you place your order at what price you will be trading
2. Closed-end fund: managed fund with specified investment policy and fixed number of shares that
trade intra-day on an organized exchange at market determined prices (can be premium/discount to
NAV)
- Difference with 1. -> fixed number of shares outstanding
- When the fund is created, they issue a number of shares (just like a company that goes
public). Once the shares are created, they will trade in the market. They trade on an
exchange.
- This also means that you can trade intra day: I can buy a share at any moment in the day, and
I know the price of the shares
- What is the drawback: the price that you pay, is not necessarily the same as nav
o You enter not at nav, but at the market price. The market price most of the time
deviates from nav; on average, prices are below nav so at a discount.
o But we do observe that there is some time variation over the life cycle of these
closed end funds. Often at the start they trade at a premium, over time they trade at
a discount
▪ There are multiple reasons to trade at a premium or discount
▪ Vb. if there is few demand, people are not willing to pay a high price to enter
the fund, so they will trade at a discount
▪ Vb. if the market believes that the manger of the fund is not very skilled,
they will trade at a discount, because no one is willing to buy the portfolio
▪ Vb. tax reasons: suppose the fund has invested in particular instruments that
have a beneficial tax treatment -> fund is attractive -> pushes prices up,
maybe above nav
3. Unit trusts: collective investment established under a trust deed with investors being the
beneficiaries.
- The investors/shareholders are actually the beneficiaries of the trust (different kind of legal
structure)
4. Exchange traded fund (ETF): hybrid format, legally structured as open-end, but traded intra-day
very close to NAV on an organized exchange
- This market becomes bigger and bigger each year
- Hybrid: combination of 1 and 2 ->
o Very similar to 1
▪ They have a varying number of shares, varies on a daily basis
▪ They trade very close to nav (not exactly but almost exactly)
o Very similar to 2
▪ Can be traded intra day, you don’t have to wait until the end of the day
o => it combines the best of the two
- ETF track particular indices (not always very passive); nowadays, there are many more
actively oriented ETF’s also
- ETF might seem very simple, but technically it is quite complex. To make sure that you have
this instrument, you have a complex system behind the ETF’s
o Means that behind the structure, you have at each moment in time a primary market
and a secondary market
o But as investor you don’t see all of that
- When you see ETF’s, you have to be careful to if it is a physical ETF or a synthetic ETF
o Physical ETF -> really has underlying the basket of assets that it is tracking;
10
Practicalities
Why should you take this course?
- Value practical implementations, not a theory course, use the theory, valuable later in the
career
- Slide: questions that we will answer
Course overview: 4 parts
- 1. Introduction
- 2. Portfolio theory: active vs. passive investing
- 3. Fixed income investing
- 4. Applied portfolio management (also guest lecture here)
You will enjoy this course if…
- Risk and uncertainty is key in investments, that is why it is hard
- Not mathematical, but some basic calculations are necessary
- About the application, not the theory
- A lot of terms we already know will be thought
Activities
- Every week one topic
- Learn by doing: participate in class
- Discussion forum on Toledo
o Structure, per topic, about lecture material or about exercises
Lecture material
- Handbook investments, bodie, kane, Marcus (13th edition) -> buy it
Lecture material
- For each topic: the slides
- Solutions to the exercises that you need to be able to solve will be on toledo
o If the solution is not there, we don’t have to know the exercise
- Some extra literature
- Excel files with solution
- Video clips
- New material: available Friday 1pm
- Recordings of the lectures (always available)
Evaluation
- Januari: exam (80%) + group assignment (20%)
- Assignment: 2 or 3 students per group (specific or random team)
o REGISTER FOR A TEAM!!!!
o DEADLINES
o Assignment will be posted by the end of October
o She will help, but only if you come as a team to her, sometimes she will even give
part of the solution, important to work as a team
o Excel assignment -> you need to be good at excel for finance jobs
- Exam January: theory and exercises
- Exam September: assignment does not count anymore
1
, o Except for students that do not participate the January exam because of overlap, and
do the exam in September
- !! Most exam questions come from the handbook (80% of the questions)
o This says you the level that you need to know
Investments: capital markets and products
= an introductory topic to give you the broad context of the class
If we talk about investments, we talk about capital markets, we talk about the products that are
traded within these markets
On the slides: chapters in the BKM that you need to know!
Background reading: not compulsory, only if you want to know more about this topic
Financial markets
The class is about investments in financial instruments, financial products
Function
Why do these financial products exist? Multiple functions of investments of financial markets
1. Share/transfer risks
- It might be that you are exposed to a financial risk, but you are not willing or unable to take
this risk, then a financial product allows you to transfer that risk
- In practice: Most people tend to overestimate their risk bearing capacity. Most people think
that they like risk, that they can bear the risk; that their risk aversion is low; however in
reality, this is not the case. People take on risk, assuming that they can bare the risk, and
when the risk materializes, they panic. Panic is the worst environment to take decisions, the
worst decisions are made in a period of stress
- This is why it is important to understand your risk appetite
- How does it come that people tend to overestimate their risk bearing capacity?
o 1. Biases
▪ Behavioural finance, we do observe some difference in risk taking behaviour
vb. male vs. female
o 2. People are a bit blind for risk. There is a trade off between expected return and
risk, one thing does not come without the other. People tend to ignore the risk
component and are extremely focussed on the return component.
▪ Of course I prefer more return, but then they forget about the fact that more
return = more risk
▪ Overly focussed on the return, and forget the risk
o 3. Hard to understand what risk is
▪ What is risk? Two key concepts
▪ The fact that there are multiple outcomes -> no certainty, but probabilities;
you don’t know ex ante which outcome will materialize
▪ At least one of the outcomes is harmful.
• BUT being less than expected is not necessarily harmful
• Suppose: someone gives me 100, 200 or 300 euros, all with different
probabilities. I have an expected return (150), I could end up with
less than I expected => does not mean it is a risk; because all of the 3
scenario’s are good scenario’s
▪ Intuitive definition in normal situations: Risk is really about the likelihood
that something bad/harmful can happen to you -> this is not the definition of
risk in finance
▪ Definition in finance of risk:
2
, • We use volatility in the definition of risk. How does volatility fit in
that more intuitive definition of risk? Not straightforward, you need
statistical knowledge to do that. Many investors do not have that
knowledge, or they have the knowledge but they do not necessarily
make the translation.
• What does she mean by that? If you think about probabilities of
different outcomes and one of the outcomes being negative/harmful
-> this means that you end op with a description that is more
broader than just volatility
• Expected return is the first moment. Volatility is ultimately the
second moment of your distribution
• But the intuitive definition is more about the whole distribution.
Why do we typically work with expected return and volatilities?
Because we assume normal distributions. And we have normal
distributions the first two moments define our distribution. But if
you just limit yourself to these two moments, you might forget what
it really means in terms of the different outcomes that can happen
to you and the likelihood of these outcomes. But it is still there.
• Simple example about this
Vb. we have an investment, vb. you buy a stock
- Typical expected return on an annual basis
o ! always work on an annual basis, if an expected return of volatility is not annualized,
annualize it, because you typically have intuition for annual numbers
- What would be a typical expected return and volatiltiy on a single stock investment?
o E(R) = 13% = expected return on an annual basis
o σ(R) = 33% = volatility on an annual basis (not of a diversified portfolio, but on a
single investment)
- What does that mean if you invest in this asset? Lets impose a normal distribution
- Tekening
o So this is probably much more informative than just looking at the expected returns
and volatilities to understand whether your able to bear a particular amount of riks
o Now you know that If you take on this investment, it means that you have a 16%
chance to end up with a return lower than -20%
o Once you impose a distribution and you look at the probabilities associated with the
different outcomes, it becomes much more easy to grasp whether you are able to
bear the risk
o ! in reality returns are not normally distributed, it is worse, because there is more
mass in the tails (extreme negative or extreme positive returns)
▪ Being skewed is not necessarily bad, only if it is to the left (more negative
probabilities)
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,VERDER: why do these products exist
2. Financial markets allow to separate the timing of income (when you get the income) and
consumption (when you want to consume the income): store wealth to transfer to the future
o Financial products allow you to make an advance on future income
o Vb. taking out a loan or obligation
o If you buy a bond, you transfer your storewealth to the future
o Transferring wealth over time allows you to smooth consumption (no peaks and
valleys in the consumption pattern)
3. Financial markets allow to separate ownership and management in support of large-scale
businesses (but be careful with associated agency problems)
o Without financial markets, companies would not be able to grow as much as they do
today.
o A firm might not have sufficient means to take the next step in their growth process,
because they don’t have the funding that they need. Financial markets can help
them secure that funding to grow
4. Financial markets allow to allocate resources efficiently i.e. to most productive real
investments (= informational role of financial markets)
o Efficiency of a market
o Which crucially depends upon the degree of efficiency
o Market efficiency: markets are efficient if all relevant information is reflected in
prices
o Often when we think about market efficiency, we immediately think about arbitrage
opportunities; if a market is not efficient, there are arbitrage opportunities
o But the degree of market efficiency is much more important than trading
opportunities, whether you can re… arbitrage profits; it all has to do with an
allocation of resources -> if the market is not efficient, too few money goes to
particular investments, and too much money to others -> only when the market is
efficient, the different opportunities get the money that they deserve
o Market efficiency is really important -> not just for the investors or for arbitrage, but
for the economy to grow in a sustainable way
Asset classes
If you think about the different products/instruments that are traded/that exist, there exists a large
range of products.
In this opleidingsonderdeel, we will limit to very standard products, mainly two big asset classes
- Money market instruments
o = short term debt security with low risk
o She will talk about it as ‘the risk free’
o Some are actually riskier than others within this class, but as compared to other
assets in the economy, they are the risk free instruments
o Vb. cash, products that allow you to save
- Capital market instruments
o Here we typically have longer term instruments, could be debt (bonds ) and equity
(stocks)
o When prof refers to investing, she means this
Each instrument is unique in terms of (un-)certainty of payments (how likely the payments are) and
timing of payments (when you can receive the payements) and has a distinct contribution to the
investment portfolio
- Unique risk return profile
- This makes that the different instruments all have a different role to play in a portfolio
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, - This is why, when we think of a diversified portfolio, consists of stock AND bond
1. Money making instruments
List of the instruments that you can regard as a money making instrument:
- Treasury bill (T-bill): government debt obligation with a maturity < 1 year
o Short term debt, issued by the government
- Certificate of deposit (CD): time deposit at a bank
- Commercial paper (CP): short term unsecured debt issued by a large corporation
o You need to have good credit quality, to be able to issue this CP
- Bankers’ acceptance: a bank promise to pay a prespecified amount
- Repurchase agreement (repo or RP) and reverse repo: a short term loan (usually overnight)
using other securities (usually government securities) as collateral
o Repo could also be seen as a spot sale of securities combined with a forward
purchase of securities
- Interbank loans: short term loans among banks (from which reference rates are being
calculated e.g. ESTR, EURIBOR)
o Loans in between banks, wholesale market, interbank market
o ESTR rate = overnight rate in euros
▪ Libor scandal 2014 -> change in reference rates -> so ESTR rats is a new rate
▪ Before? Bank were being asked: at what rate would you be willing to lend to
someone else
▪ What is new in the ESTR rate? Effective rate, average rate that was charged
to one another
o EURIBOR = can go from one week up to one year
- Central bank deposits and loans: short term deposit/loan of a bank by its central bank
o Internet: The main refinancing operations rate is the interest rate banks pay when
they borrow money from the ECB for one week
o Risk free, not for retail investor, but for institutional investors
o Central bank deposits an loans; deposits for the loans that banks/fin institutions do
with the central bank
▪ Vb. Central bank in USA -> federal funds
▪ Vb. for Europe (ECB) -> MRO (main refinancing operations)
▪ Vb. deposit facilities, lending facilities (short term = one week), MRR
(marginal reserve requirements)
o It are these policy rates that used to be negative for a while
▪ When banks deposited money at the ECB, they needed to pay for this
(negative rates)
▪ Nowadays sinds 2022 it is back to zero, and now it is positive again
- Call loans: loans that need to be repaid, on demand at any time; often made by banks to
brokerage firms to fund individuals that buy on margin
o Brokerage firm (internet): fin instelling die als tussenpersoon optreedt bij het kopen
en verkopen van beleggingen. Deze bedrijven bieden investeerers toegang tot fin
market en kunnen handelstransacties namens hun klanten uitvoeren
o To buy on margin (internet): geld lenen van een broker om een belegging te doen;
het onderpand vanhet geleende bedrag zijn de beleggingen. Je kan dus meer
investeren dan je hebt omdat je kan lenen (zie verder)
o Clients that want to leverage their portfolio, need to take out a loan. The brokerage
firm gives the loan, but actually the brokerage firm takes out a loan at a bank = call
loan
- Savings deposit
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,Most money market instruments are low risk, but they are not risk-free!
- They are not all equally risk free
- When all things go well, the difference in risk between them is small; but in times of stress,
spreads will increase
- In general T-bills (government bond) have lowest risk, both in terms of credit risk, as well as
liquidity risk
Figure about the spread between the different rates
- TED Spread = difference between the T-bill and the LIBOR rate
- Both move quite equally but in moments of crisis, the spread increases drastically
- Vb. financial crisis 2008 & covid 2020, TED Spread spiked -> higher liquidity and credit risk of
the LIBOR rate
2.1 Capital market instruments: bonds (debt)
Key concepts here:
- Longer term debt instruments with wide range of maturities
o It can be 1 year, but also 10, 20, 30… years
- Various credit qualities: from high credit-quality instruments to (very) low credit-quality
(junk) instruments
o Different bonds: bonds with high credit quality (vb. investment grade bonds), bonds
with low credit quality (junk bonds)
o When you make an investment, you need to check the credit quality
o If they offer you high coupons, then you know that the credit quality will be poor;
you need to be offered high returns, high yields, otherwise you won’t buy that
instrument
- Liquidity varies from very high to almost zero
o Some bonds are very liquid vb. government bonds
o Some bonds can be very poor, low -> extra risk -> if you want to step out, you might
have a hard time finding a counterparty or you will only be able to sell off the bond
at a discount
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, - Often in smaller denominations such that they can be held by retail investors
o It is because of the small denominations that the instruments are also attractive to a
retail audience
- Often not traded on the exchange, but rather traded over the counter (OTC) via dealers
- Expressed as a % of the par value
o Par value = nominal value
o Then we don’t have to refer to the denomination. You can get a good grasp of what
the price really is (cheap or expensive)
o Vb. it you say ‘the bond is traded at 95%’, you know that it trades at 95% of its par
value
- Typically pay coupon interest (annual or semi-annual)
o Bonds pay coupon interest, on an annual or semi-annual basis
o Vb. if we have a bond that pays out coupon at 6% -> at one point in time you receive
6% of the nominal value as a coupon. If the 6% is on a semi-annual basis, every 6%
you get 3%
- Performance measurement: hpr or yield with (including a risk premium for credit risk)
o When you want to measure the performance of a bond, we will see in this class
numerous ways to calculate the return. It depends on the instrument, and what the
kind of metric is you are looking for.
o It could be a holding period return, vb. the return that you earn when you buy the
bond today and sell it off tomorrow
o It could be some kind of yield concept. A yield = internal rate of return;
▪ vb. Yield to maturity = assumes that you hold on to the bond up until
maturity
▪ vb. yield to call, if you have a callable bond
▪ vb. current yield
o we will see which concept is used in which circumstances. Because for some bonds,
talking about yield to maturity doesn’t make sense and you need another concept
vb. yield to call
different kinds of bonds, depending upon the identity of the issuer
- Treasury notes: government debt with 1 yr < maturity < 10 yrs
o Up until 10 years
- Treasury bonds: government debt with maturity > 10 yrs
o More then 10 years
o But you can refer to all of them as a bond (also the notes)
- Treasury inflation-protected securities (TIPS): government debt with principal and interest
adjusted for inflation
- Federal agency/municipal bonds: debt issued or guaranteed by, respectively, a federal
agency, state or local government
- Corporate bonds: debt issued by a large corporation; typically larger default risk as compared
to government debt; options included (callable, convertible)
- Asset backed debt: proportional ownership claim in a asset pool (cf securitization)
o This gives u some ownership
o Not one particular issuer, but a pool of assets
2.2 Capital market instruments: stocks (equity)
Stocks (common shares) are issued by corporations and represent ownership in a firm (stock gives
you ownership in a firm)
- share the distribution of profits
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, - have voting power at shareholders’ meeting (this makes it different from a bond, a bond only
has financial returns)
Equity represents a residual claim: you only receive payout if all other claims (e.g. salaries, debt,
taxes) are paid (the last one to be paid)
- Because of the residual claim, equity is more risky than bonds
- At the end of the pecking order
Equity has limited liability: minimum share price is zero (return is bounded at -100%)
- Limited liability: If the firm goes bankrupt, even tough you are a shareholder, you are not
liable with your own wealth (you can loose it al but not more than you put in yourself)
- This is important legally, but also for finance theory or modelling this is important. The fact
that equity has limited liability, says something about which distribution is appropriate.
o Earlier we assumed the normal distribution of the returns
o Is this in line with limited liability? No, because you cannot go in the minus and the
rang of a normal distribution is [-infinity, + infinity] -> prices can go negative
o So the normal distribution is not appropriate to talk about returns for shareholders
o How do we solve this? Sometimes we just work with a normal distribution and ignore
this fact, because it is true that the likelihood of ending deep in the negative tail is
small. But sometimes we do solves this -> two things that we could do when
modelling returns and we want to work with the normal distribution
▪ 1. We use log-returns -> you cannot take a log of a negative number, so by
definition, the prices cannot go below zero
▪ 2. What is the frequency of the returns? Daily returns -> then you naturally
put boundaries on the distribution, because the likelihood that on a daily
basis your return is less than 100% becomes extremely small
• Whether you calculate a daily return or a daily log return, the
numbers are approximately the same
• But if you lengthen your horizon: an annual return and an annual log
return -> those numbers are not the same
• Only use log returns when you work on a daily basis, when the
frequency is high
o => this is how we can incorporate the limited liability in finance theory
Performance measurement: return (mostly reward for market risk)
- We will calculate returns, just the difference in prices
Note: preferred shares are related and possess common equity features, but also bond features
(combination of bond and equity):
- share of ownership (like stocks)
- no voting power (like bond)
- promise of fixed dividend (often cumulative) (like bond)
Investment funds
Having introduced the basic financial instruments, many retail investors and even also institutional
investors will not necessarily trade individual instruments. They will trade funds, they invest in a fund
(whatever the underlying structure is).
People often invest in a pool, this allows them to profit from economies of scale
- They then have ownership in this pool of assets
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,Benefits
- Diversification and divisibility
o As a part of this larger pool, you can more easily diversificate. Because the amount
that you have can be small, but in a pool, you can diversificate
o Divisibility = deelbaarheid
- Lower transaction costs
o Entering a fund is costly, but within the fund the transaction costs will be lower,
because they will be able to trade at more beneficial …spreads as compared to you
- Professional management
o They have tools at their disposal to manage this portfolio in professional in a timely
fashion
- Record keeping and administration
o This is mainly important in foreign investments
Net asset value
= important concept in funds
Gives you an idea of what a share in the fund is worth. It is the
- (market value of assets – liabilities) / shares outstanding
- If the NAV increases, your investment becomes worth more
When the composition of the fund is changed (when they buy/sell), this leads to a turnover
- Keep track of the turnover of the fund as an investor, because turnover generates
transaction costs. If the fund turns over a lot, it might eat up your return
- Different turnover rate, depending upon the investment strategy. If you have the two big
classes:
o Passive investment -> very low turnover, low transaction costs
o Active investment -> turnover can be a lot, high transaction costs
o Behavioural biases -> male managers turn over more than female managers doe
o If you turnover because there are good investment opportunities, that is fine, but if
you turnover just because of the fun of being active and making investment
decisions, this will be expensive for the ultimate investors/owners
- Turnover rate = market value of asset sold / market value of assets
Investment companies
Now if we talk about the fund, there are many different structures.
1. Open-end fund (’mutual fund’): managed fund with specified investment policy that issues new
shares when investors buy in and redeem shares when investors cash out; they are priced at NAV
(traded at day-end only)
- Most of the time, when someone talks about a fund, it is about a mutual fund
- The number of outstanding share changes upon demand. If there are more investors that
want to step in, new shares are being created. If more investors want to step out, shares are
being redeemed
o So the number of shares outstanding is not fixed, but varies with the interest in the
fund
- This makes that the open end funds, they trade at NAV -> when you want to step in, you pay
the nav, really what it is worth
o But you will not be able to trade them intra day, you will not be able to buy them in
the market, you buy the immediately from the fund
o This means when you want to place an order in the fund, you do not know at which
price you will be able to buy, because the nav is only calculated at the end of the day,
and then everyone who wants to step in/out will trade at that nav
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, - => you cannot trade quickly, you cannot trade intra day and you do not know in advance
when you place your order at what price you will be trading
2. Closed-end fund: managed fund with specified investment policy and fixed number of shares that
trade intra-day on an organized exchange at market determined prices (can be premium/discount to
NAV)
- Difference with 1. -> fixed number of shares outstanding
- When the fund is created, they issue a number of shares (just like a company that goes
public). Once the shares are created, they will trade in the market. They trade on an
exchange.
- This also means that you can trade intra day: I can buy a share at any moment in the day, and
I know the price of the shares
- What is the drawback: the price that you pay, is not necessarily the same as nav
o You enter not at nav, but at the market price. The market price most of the time
deviates from nav; on average, prices are below nav so at a discount.
o But we do observe that there is some time variation over the life cycle of these
closed end funds. Often at the start they trade at a premium, over time they trade at
a discount
▪ There are multiple reasons to trade at a premium or discount
▪ Vb. if there is few demand, people are not willing to pay a high price to enter
the fund, so they will trade at a discount
▪ Vb. if the market believes that the manger of the fund is not very skilled,
they will trade at a discount, because no one is willing to buy the portfolio
▪ Vb. tax reasons: suppose the fund has invested in particular instruments that
have a beneficial tax treatment -> fund is attractive -> pushes prices up,
maybe above nav
3. Unit trusts: collective investment established under a trust deed with investors being the
beneficiaries.
- The investors/shareholders are actually the beneficiaries of the trust (different kind of legal
structure)
4. Exchange traded fund (ETF): hybrid format, legally structured as open-end, but traded intra-day
very close to NAV on an organized exchange
- This market becomes bigger and bigger each year
- Hybrid: combination of 1 and 2 ->
o Very similar to 1
▪ They have a varying number of shares, varies on a daily basis
▪ They trade very close to nav (not exactly but almost exactly)
o Very similar to 2
▪ Can be traded intra day, you don’t have to wait until the end of the day
o => it combines the best of the two
- ETF track particular indices (not always very passive); nowadays, there are many more
actively oriented ETF’s also
- ETF might seem very simple, but technically it is quite complex. To make sure that you have
this instrument, you have a complex system behind the ETF’s
o Means that behind the structure, you have at each moment in time a primary market
and a secondary market
o But as investor you don’t see all of that
- When you see ETF’s, you have to be careful to if it is a physical ETF or a synthetic ETF
o Physical ETF -> really has underlying the basket of assets that it is tracking;
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