Lesson 1: Risk, Return and the Historical Record

Question 1

What factors determine the level of interest rate?

Answer 1

• Supply from funds of savers (pool of loanable funds)
• Businesses demand for borrowing money
• Monetary policy of governments / central banks
• Expected rate of inflation

Question 2

What is the nominal interest rate?

Answer 2

The growth rate of money

Question 3

What is the growth rate of money

Answer 3

Nominal interest rate

Question 4

What is the growth rate of purchasing power?

Answer 4

Real interest rate

Question 5

What is the real interest rate?

Answer 5

The growth rate of purchasing power

Question 6

How does the Consumer price index get calculated?

Answer 6

It measures purchasing power by averaging the prices of goods and services in the consumption basket of an average family.

Question 7

What does the Consumer price index (CPI) measure?

Answer 7

Purchasing power (or change of it over time) as expressed in inflation i

Question 8

Equilibrium Real Rate of Interest: Fund Demand Increases

Answer 8

Demand curve shifts to the right, IR Equilibrium increases to get more funds lent

Question 9

Equilibrium Real Rate of Interest: Fund Demand Decreases

Answer 9

IR drops as there is a sufficient large pool of funds

Question 10

Equilibrium Real Rate of Interest: Fund Supply Decreases

Answer 10

IR increases, can happen if FED has an contractionary monetary policy

Question 10

Equilibrium Real Rate of Interest: Fund Supply Increases

Answer 10

IR decreases as there are more funds to lend, can arrive if the FED has an expansionary policy

Question 11

Fisher Equation

Answer 11

(1+r_nominal) = (1+r_real)*(1+i)

Question 11

Approximation of the Fisher Equation

Answer 11

r_nominal = r_real + i

Question 12

Solve Fisher Equation for r_real

Answer 12

(1+r_nominal) / (1+ i ) - 1 = r_real

Question 13

What asset is a CD?

Answer 13

A Certificate of Deposit is a type of savings account that pays a fixed interest rate on money held for an agreed-upon period of time.

Question 14

Formulas for real after tax rate with r_nom

Answer 14

r_nom * (1 - t) - i

t = tax rate

Question 15

Formulas for real after tax rate with r_real

Answer 15

r_real * (1 - t ) - i * t

t = tax rate

Question 16

After tax real return in an inflation protected tax system

Answer 16

1. r_real = r_nom - i
2. r_real * ( 1 - t )

Question 17

After tax real return in a none inflation protected tax system

Answer 17

r_nom * ( 1 - t ) - i

Question 18

What is the Risk Premium?

Answer 18

The additional return expected by investors for taking on higher risk compared to a risk-free asset. (return is expected)

Question 19

What is the risk free rate?

Answer 19

The risk free rate is the rate earned on a risk free asset such as
T-bills, money market funds, or the bank

Question 20

What is excess return?

Answer 20

The difference in any particular period between the actual rate of
return on a risky asset and the actual risk free rate is called the
excess return. (Return is realised)

Question 21

Risk premium formula

Answer 21

r_p = E(r) - rfr

Question 22

Risk Aversion

Answer 22

The degree to which an investor is unwilling to take on risk.
Risk averse investors always require a positive risk premium, otherwise they would not invest.

Question 23

What is Sceneario Analysis

Answer 23

• Determine a set of relevant scenarios & associated returns
• Assign probabilities to each
• Conclude by computing
  – The risk premium (reward)
  – Standard deviation (risk)

Question 24

What is a time series?

Answer 24

• Are assets returns histories (realized returns)
• Do not explicitly provide investors’ original assessment of the probabilities of those returns
• Only Holding Period Returns can be observed

Question 25

Holding Period Return Formula

Answer 25

HPR = [ E(P₁) - P₀ + E(D₁) ] / P₀

HPR = Holding period return
P₀ = Beginning price
E(P₁) = Expected ending price
E(D₁) = Expected dividend during period one

Question 26

Expected Returns Formula

Answer 26

E(r) = Σ_s p(s) * r(s)

Σ_s = Sum of states
p(s) = Probability of a state
r(s) = Return if a state occurs
s = State / scenario

Question 27

Expected Returns / the Arithmetic Average Formula

Answer 27

1/n * ⁿΣ_s=1 r(s)

sum of all return of states

Question 28

Terminal Value Formula

Answer 28

TV_n = (1+r₁)*(1+r₂)…(1+r_n)

Question 29

Geometric Average Formula

Answer 29

g = TV^{1/ n}_n - 1

TV = Terminal Value

Question 30

What is the standard deviation?

Answer 30

The variance of the rate of return is a measure of volatility,
measuring the dispersion of possible outcomes around the expected value

Question 31

Variance (VAR) Fomula

Answer 31

σ² = Σ_s p(s) * [ r(s) - E(r) ]²

Sum of all state returns deviation from the average squared weighted by

Question 32

Standard deviation Formula (STD)

Answer 32

STD = √σ²

Question 33

What is the Reward to Volatility (Sharpe) Ratio

Explanation and Formula

Answer 33

The trade-off between reward (risk premium) and risk
(Standard Deviation SD)
It is a reward to volatility measure
Sharpe Ratio = Risk Premium / SD of excess Returns

Question 34

The thre STD on the normal distribution

Answer 34

1σ = 68.26%
2σ = 95.44%
3σ = 99.74%

Question 35

What is there to know about risk measurements in normal distributions?

Answer 35

• SD is a complete measure of risk
• The Sharpe Ratio is a complete measure of portfolio performance

Question 36

What is there to know about risk measurements in non-normal distributions?

Answer 36

• SD and the Sharpe Ratio are not anymore complete measures
• Deviations from normality of asset returns are potentially significant and dangerous to ignore
• Skewness and Kurtosis are an indicator if a distribution is normal or non - normal

Question 37

What is skewness in statistics?

Answer 37

kewness is a measure of asymmetry in a probability distribution. It indicates the extent to which data deviates from a perfectly symmetrical distribution.
Key points:

Positive skew: longer tail on the right side, mean > median
Negative skew: longer tail on the left side, mean < median
Zero skew: symmetrical distribution (e.g., normal distribution)
Affects risk assessment and financial modeling

Question 38

What is the Skewness formula TODO

Answer 38

TODO

Question 39

What is kurtosis in statistics?

Answer 39

Kurtosis measures the “tailedness” of a probability distribution, indicating the presence of extreme values or outliers compared to a normal distribution.
Key points:

Measures the combined weight of the tails relative to the center of the distribution
Normal distribution has a kurtosis of 3 (often referred to as mesokurtic)
Excess kurtosis = Kurtosis - 3 (to compare with normal distribution)
Leptokurtic: Kurtosis > 3, heavier tails, higher peak
Platykurtic: Kurtosis < 3, lighter tails, flatter peak

Applications: Used in risk management, financial modeling, and assessing the likelihood of extreme events in data sets.

Question 40

What is the kurtosis formula TODO

Answer 40

TODO

Question 41

What is Value at Risk (VaR)?

Answer 41

Commonly used risk measurment tool
(in regulations of banks)
TODO

Question 42

What is Lower partial standard deviation?

Answer 42

Consider negative outcomes seperatly
Considers deviations of returns from the risk free rate
It uses only bad returns and negative deviations from the risk free rate

Question 43

What is the sortino ratio

Formula and explanation

Answer 43

Similiar to sharpe ratio but replaces STD with LPSD

Sortino Ratio = average excess return / LPSD