## Question

Financial advisor Ole Olsen has received the following nominal salary in the last 4 years, cf. table 1.1 below:

Table 1.1: Ole Olsen’s salary in nominal terms

2014 2015 2016 2017

Annual salary in the

year’s prices beginning

of the year (DKK) 350,000 390,000 440,000 510,000

Problem 1.1

Calculate the annual increase (in percent with two decimal places) in Ole Olsens nominal salary in the years 2014, 2015 and 20161.

Ole Olsen wants to be healthy, therefore he eats organic oatmeal for breakfast and spends the most of his salary on this. The price of 1 kilo organic oatmeal in nominal prices in the last 4 years are stated in table 1.2 below:

Table 1.2: Price of 1 kilo organic oatmeal in nominal terms

2014 2015 2016 2017

Price of 1 kilo oatmeal

beginning of

the year (DKK) 11.50 11.80 12.15 12.50

It is assumed that the price changes of organic oatmeal reflect the inflation in each

year.

Problem 1.2

Calculate the rate of inflation2 (in percent with two decimal places) in the years 2014, 2015 and 2016, based on the price changes on organic oatmeal.

Problem 1.3

Calculate Ole Olsen’s increase in salary in real terms3 (in percent with two decimal places) in the years 2014, 2015 and 2016.

Problem 1.4

Calculate Ole Olsen’s salary in real terms in the years 2014, 2015, 2016 and 2017 with the price level beginning of 2014 as the base.

Problem 2

Table 2.1 contains information about a given financial asset X in 5 different states of

the world at time t = 1.

Table 2.1: Value (DKK) of asset X at time t=1

State Probability (p) Value of asset X

1 0.03 25.00

2 0.30 21.00

3 0.28 14.00

4 0.29 8.00

5 0.10 2.00

In all 5 states, the owner of asset X receives a cash flow of DKK 3 in the next period ]t=0, t=1[. The price of asset X is now DKK 14 (t=0).

Problem 2.1

Calculate the return of asset X in each of the five states. The correct answers must be stated as a decimal number rounded to 4 decimal places.

Problem 2.2

Calculate the expected return of asset X in the next period. As the input for your calculation you must use the rounded answers from problem 2.1. The correct answer must be stated as a decimal number rounded to 4 decimal places.

Problem 3

Assume that you are in Gebitrara, which is an economy, where the annual risk-free rate is 1.66%. In Gebitrara, the financial market is a normal market.

In Gebitrara all investors agree that in a year (t=1) there is only 2 possible states of the economy - boom and recession. The probability of a boom is 40% and the probability of a recession is 60%.

For one unit of the risk-free asset you receive DKK 920 in one year.

Problem 3.1

Calculate the price (t=0) of the risk-free asset in DKK. The correct answer must be given with 0 decimal places and this answer must be used in the next problems as well.

In Gebitrara, the price today (t=0) of the market portfolio4 is DKK 1,100. For one unit of the market portfolio, you receive DKK 1,700 in a year if the economy is in a boom, and DKK 800 if the economy is in a recession.

Problem 3.2

Calculate the expected return of the market portfolio next year. The correct answer must be given as a decimal number with 4 decimal places.

Problem 3.3

Calculate the expected cash flow from the market portfolio next year (t=1).

In Gebitrara, asset A is also traded. For one unit of asset A you receive DKK 1,505 in year when the economy is in a boom, and DKK 830 when the economy is in a recession.

Problem 3.4

Calculate the price today (t=0) of asset A.

## Solution Preview

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Problem 1.1.The annual increase in salary (note that the problem states the salary at the beginning of the year, therefore the first increase is meant during the 2014):

2014: 390,000/350,00 – 1 = 11.43%

2015: 440,000/390,000 – 1 = 12.82%

2016: 510,000/440,000 – 1 =25%

Problem 1.2

The rate of inflation:

2014: 11.80/11.50 -1 = 2.61%...

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