Week 2

Question 1

Why do we use a time subscript for returns

Answer 1

• Returns vary over time as a time series

Question 2

Define simple net returns excluding dividends

Answer 2

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Question 3

Define simple gross returns excluding dividends

Answer 3

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Question 4

What is the difference in how net and gross simple returns are expressed

Answer 4

• Net: Expressed as a percentage
• Gross: Expressed as a growth factor

Question 5

How do we calculate the gross cumulative return and give an example

Answer 5

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Question 6

In practice how would we typically compute returns

Answer 6

• From a price series
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Question 7

Define the total simple return including dividends

Answer 7

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Question 8

What does the total return show compared to the price return

Answer 8

• The total return shows how much richer an investor is after updating the market value of what is held AND after receiving a cash dividend

Question 9

Define the total simple gross returns

Answer 9

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Question 10

Define a two period total gross return

Answer 10

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Question 11

Why are nominal prices not suitable to compare across periods and countries and what can we use instead

Answer 11

• Nominal returns use nominal prices which do not account for inflation
• Countries and periods differ with inflation so it needs to be accounted for using real returns

Question 12

Define the real price

Answer 12

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Question 13

Define the one-period gross real return and simplify it with π

Answer 13

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Question 14

Why is the approximation R(t)real ≈ R(t)nom - π(t) poor

Answer 14

• Provides poor results when inflation is high or volatile

Question 15

Define the gross return of a Japanese investor for a USD asset

Answer 15

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Question 16

What is the intuition behind the definition of a foreign investors returns on a domestic asset

Answer 16

• Foreign curreny returns combine local asset performance and currency movenments multiplicatively

Question 17

Define how returns compound over time in terms of wealth

Answer 17

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Question 18

Define the annualised return R(a)

Answer 18

• The constant yearly return that produces the same terminal wealth
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Question 19

Define the arithmetic average return

Answer 19

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Question 20

Define the geometric average (annualised) return

Answer 20

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Question 21

What is the downfall of arithmetic mean returns

Answer 21

• It can materially overstate long-run performance when returns are volatile

Question 22

Define continuously compounded (log) returns

Answer 22

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Question 23

Define k-period log returns

Answer 23

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Question 24

Define the annualised log returns over 12 months and over T years and 12 months

Answer 24

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Question 25

Define real returns in log form

Answer 25

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Question 26

Why is it better if real returns are expressed in log form

Answer 26

- In logs "real = nominal - inflation" holds exactly, whereas in simple returns it is only an approximation

Question 27

What is the main difference in simple returns and log returns in the way they are expressed

Answer 27

- Simple returns are expressed as percentage changes and log returns and expressed as growth rates

Question 28

What is a practical reason why economists like log returns

Answer 28

- Multi-period log returns are sums not products - If prices go up and then back to the start, log returns sum to zero, which makes them convenient in econometrics and continuous time finance

Question 29

What are the two types of portfolio weights

Answer 29

- Equal Weighted (EW): each asset weight is 1/m - Value Weighted (VW): weights are proportional to market value at the start of the period

Question 30

Define a buy-and-hold portfolio with no dividends

Answer 30

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Question 31

Define the one period simpe portfolio return and define it in terms of w for value weighting

Answer 31

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Question 32

What does value-weighted represent mathematically

Answer 32

- w(i,t-1) is the market value of asset i as a fraction of the portfolio value at formation (time t-1).

Question 33

How does the definition of value weighted portfolio returns change when we switch to equal weighting

Answer 33

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Question 34

Why are beginning of period weights used over end of period weights

Answer 34

- End of period weights introduce look-ahead bias

Question 35

Define portfolio log returns and define in terms of beginning-of-period weights

Answer 35

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