1. Sustainability - Flervalsfråga Which one of the following statements is TRUE? Select one alternative:

Energy efficient company stocks commonly have a lower beta value compared to less energy efficient companies.

1, Imposing carbon taxes is a way to internalize cost of environmental issues.

2, Negative screening means that the investor excludes companies that do not meet certain pre-set criteria.

3, Impact investing means that the investor combines sustainability- and financial goals.

4, All statements are true

2. Risk and return - Flervalsfråga

Which of the following statements is FALSE? Select one alternative:

Well-diversified portfolios display market risk.

Well-diversified portfolios display high firm-specific risk.

Efficient portfolios have the highest Sharpe ratio.

Efficient portfolios are portfolios earning the highest expected return for a given standard deviation.

Individual stocks display firm-specific risk.

3. CAPM - Flervalsfråga

Which one of the following statements is FALSE in an economy where CAPM holds? 

Select one alternative:

The beta of the market portfolio does not have to be the largest of all betas

The beta of a risky asset cannot be negative

Risky assets may earn an expected return higher than the one of the market portfolio

The beta of a risky asset can be greater than one

The tangency portfolio has a beta equal to one

4. Portfolio theory and risk - Flervalsfråga

Which one of the following statements is FALSE?

Select one alternative:

The variance of the return of the risk-free asset is equal to zero

Because the return of the risk-free asset is fixed, its correlation with the market portfolio is equal to -1.

It is possible to build a portfolio of two risky assets whose return has a variance equal to zero if the correlation between the return of its components is equal to minus one

Short-selling the risk-free asset is equivalent to borrowing money at the risk-free rate through a standard loan

None of the other answers are correct. (This answer should be chosen if you consider that all the other statements are true).

5. Options - Flervalsfråga

Which one of the following statements is FALSE?

Select one alternative:

The higher the strike of a put option, the more valuable it is

The lower the strike of a call option, the more valuable it is

Put options give their holder the right to sell the underlying at a given price at a future point in time

Call options give their holder the right to purchase the underlying at a given price at a future point in time

An American-style option can only be exercised at its maturity.

6. Miscellaneous - Flervalsfråga

Which one of the following statements is FALSE?

Select one alternative:

1. The present value of a growing annuity can be computed even if the discount rate to be used is equal to its growth rate

2. An invesment project may not have Internal Rate of Return

3. There are special situations when the NPV rule may lead to the wrong investment decision

4. None of the other alternatives is correct (this answer is to be chosen if all other answers are considered to be correct)

5. The tangency portfolio is the portfolio of risky assets only with the lowest Sharpe ratio.

7. In serach of an efficient portfolio - Essä

Your portfolio consists of a full investment in just one stock, Eriksson. Suppose this stock has an expected return of 18% and volatility of 31%. Suppose further that the tangency portfolio has an expected return of 16% and a volatility of 22%. Also, assume that the risk-free rate is 5%. What is the highest possible expected return of an alternative investment that has the same volatility as your investment in Eriksson?

You need to explain how you got to your final answer in order to get points for this question. JUST TYPING THE FINAL ANSWERS WILL GIVE YOU ZERO POINTS. TYPE YOUR ANSWER AND EXPLANATIONS ON THE SPACE PROVIDED BELOW. (Express the expected return as a percentage and round your final answer to two decimal digits)

To find the highest possible expected return of an alternative investment that has the same volatility as the investment in Eriksson, we need to look for a portfolio that lies on the CML (Capital Market Line) with the same volatility as Eriksson's stock.

The CML represents the efficient portfolios that offer the highest expected return for a given level of risk (volatility), combining the risk-free asset with the tangency portfolio (market portfolio). The equation for the CML is as follows:

E(r) = rf + (vs * (Erp) - rf) /Vtp

Given data:

Expected Return of Eriksson stock (ER_Eriksson) = 18%

Volatility of Eriksson stock (σ_Eriksson) = 31%

Expected Return of Tangency Portfolio (ER_Tangency) = 16%

Volatility of Tangency Portfolio (σ_Tangency) = 22%

Risk-Free Rate (RFR) = 5%

Now, we can plug these values into the CML equation:

Expected Return (ER) = 5% + [31% * (16% - 5%) / 22%]

Expected Return (ER) = 5% + [31% * 0.5]

Expected Return (ER) = 5% + 15.5%

Expected Return (ER) = 20.5%

So, the highest possible expected return of an alternative investment with the same volatility as Eriksson's stock is 20.5%.

8. Dividend policy - Essä

A company announces a change of dividend policy soon after paying a dividend equal to 8 per share. The company decides to retain part of the dividends for next year in order to invest in a project which will create a higher dividend growth. Its dividend next year will thus be equal to 3 per share and it will grow at a rate of 4% in subsequent years. Just before the announcement (but right after the dividend was paid) the stock of the company had a price equal to 100 and its previous dividend growth rate was equal to 1%. What is the price of the stock after the announcement if the cost of equity remains unchanged?

(Round your answer to the nearest whole number)
You need to explain how you got to your final answer in order to get points for this question. JUST TYPING THE FINAL ANSWERS WILL GIVE YOU ZERO POINTS. ANSWER ON THE SPACE PROVIDED BELOW.

to calculate the stock price after the announcement of the new dividend policy, we can use the "Constant Dividend Growth Model".

The formula for it is:

Po = Div1 / (rE - g)

Po = current stock price.

Div1 = dividend expected to be paid at the end of the next period.

rE = "Cost of equity" (required rate of return)

g = dividend growth rate

Step 1:

Po (current stock price) =

(Dividend equal to 8 per share) * (1 + previous dividend growth rate) / (Stock price before dividend)

= Cost of equity

Po = 8 * (1+0.01) / 100 = 0.09

Step 2:

Po = (next year dividend (3 per share)) / (Cost of equity - New dividend growth rate)

Po = 3 / (0.09 - 0.04) = 3 / 0.05 = 60

Answer: current stock price is 60.

9. Time value of money -

What is the present value of recieving 3500 SEK in 6 years and 6 months from now, assuming an annual discount rate of 4.2 percent? (Answers are rounded to the nearest integer) Select one alternative:

PV = FV / (1+r)^n

PV = 3500 / (1+0.042)^6,5

PV = 3500 / 1,311215

PV = 2678, 723398

PV = 2679 SEK 

10. The security market line

Assume that CAPM applies. Suppose that you know that the Stock of a company called "Not at all" has a beta equal to 0.9 and a risk premium equal to 12%. The risk-free rate happens to be equal to 2%.

What is the risk premium of the stock of another company called "Nothing to worry about" if it has a beta equal to 1.5?

The CAPM formula to calculate the expected return of a stock is as follows:

E(R) = Rf + B * (E(Rm)) - Rf)

E(R) = expected return of the stock.

E(Rm) = expected return of the market

Rf = risk-free rate

B = beta coefficient of the stock.

Info from the question:

Beta (B) of “Not at all” company´s stock: 0.9

Beta of “Nothing to worry about” company's stock: 1.5

Risk premium of “Not at all”: 12%

Risk-free rate: 2%

Step 1:

You can first calculate the expected return of the market (E(Rm)) using the risk-free rate and the risk premium of “Not at all” company´s stock:

E(Rm) = Rf + risk premium = 

2 + 12 = 14%

Step 2:

Now you can use the CAPM formula to calculate the expected return of “nothing to worry about”.

E(R) = Rf + B * (E(Rm) - Rf) =

E(R) = 2% + 1.5 * (14% - 2%) = 20%

11. FCF Model (Free Cash Flow Model):

A company is expected to generate the following free cash flows over the next four years:

Year                 |1  |       2|     3 | 4 |

FCF (in millions) | 51.5 | 69.7 | 77.3 | 76.5 |

After that, the free cash flows are expected to grow at the industry average of 3.6% per year (g). If the weighted average cost of capital (WACC) is equal to 13.1%, what is the firm's value?

(Answers in millions rounded to the closest whole number)

Step 2:

FCF year 1 / (1 + WACC)^1 + 

FCF year 2 / (1 + WACC)^2 + 

FCF year 3 / (1 + WACC)^3 + 

FCF year 4 / (1 + WACC)^4 = A

Step 3:

PV = 51.5 / (1+0.131)^1 = 45.53492485

PV = 69.7 / (1+0.131)^2 = 54.48884073

PV = 77.3 / (1+0.131)^3 = 53.43080029

PV = 76.5 / (0.131 - 0.036) = 805.2631579

805.2631579 * 1 / (1+0.131)^3 = 556.6087319

Value of the firm = 45.53492485 + 54.48884073 + 53.43080029 + 556.6087319 = 710. 0632978

12. Zero-coupon bond and YTM - Flervalsfråga

A zero-coupon bond with maturity in six years and face value 1000 SEK has a price equal to 733 SEK. What is its yield-to-maturity? (Answers rounded to two decimal digits)

Yield-to-maturity (YTM) för en nollkupongobligation kan beräknas med följande formel:

P = F / (1 + r)^n

där:

P = är nuvärdet (priset) på obligationen.

F = är obligationens nominella värde (face value).

r = är den årliga räntan (yield-to-maturity).

n = är antal år till förfall.

I det här fallet har vi:

P = 733 SEK

F = 1000 SEK

n = 6

Vi behöver lösa för r:

733 = 1000 / (1 + r)^6

Låt oss nu lösa denna ekvation för r:

Isolera (1 + r)^6

(1 + r)^6 = 1000 / 733

Beräkna 1000 / 733

1000 / 733 = 1.364

3. Ta den sjätte roten ur båda sidorna för att lösa för r:

1 + r = (1.364)^1/6

4. Beräkna (1.364)^1/6

Beräkna först på miniräknaren eller excel (1/6) som är = 0,1666666667.

(1.364)^0,1666666667

1 + r = ca 1.0531

5. Subtrahera 1 från båda sidor:

1 + r = ca 1.0531

r = ca 0.0531

6. Konvertera till procent:

r = ca 5.31%

Så yield-to-maturity (YTM) för denna nollkupongobligation är 5.31%, vilket stämmer med facit.

13. Payback period - Flervalsfråga

You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost 5050 and it will be posted for one year. You expect that it will generate additional revenue of 645 per month. The discount rate is 5%.

What is the payback period?

(Answers rounded to two decimal digits)

To calculate the payback period for the investment:

1. Identify the initial investment and monthly revenues: 

Initial investment: 5050

Monthly revenues: 645 per month

2. Calculate the payback period:

Payback period =

Initial investment / Cash flows (monthly revenues)

Payback period =

5050 / 645 = ca 7.83 (months)

3. Perform the division:

   Payback period = 5050 / 645 = ca 7.83 (months)

Answer:

payback period is approximately 7.83 months.

14.

Equivalent Annual Annuity - Flervalsfråga

A company is considering a project that requires an initial outlay of 2050 SEK. The project will produce a first cash-flow of 500 SEK at the end of year 1 and then the subsequent yearly cash-flows will grow at a rate of 1% per year. The project has a lifespan of 8 years. Suppose that you know that the EAR rate is equal to 3.5%.

What is the EAA of this project? (Answers rounded to two decimal digits)

Info/data:

Initial outlay: 2050

First cashflow: 500

Growthrate: 1%

Lifespan: 8

EAR: 3,5%

Step 1: Start to calculate the PV of Annuity

First cashflow * (1 / (EAR - Growthrate))

* (1 - ((1 + Growthrate))

/

(1 + EAR))^Lifespan

= 

500 * (1 / (0.035 - 0.01))

* (1 - ((1 + 0.01))

/

(1 + 0.035))^8

= PV of Annuity = 3553

Step 2: Räkna ut NPV

PV of Annuity - Initial outlay =

3553 - 2050 = 1503

Steg 3: Räkna ut EAA

EAA =

NPV / ((1 / EAR) * (1- (1 + EAR)^Lifespan)) = 

1503 / ((1 / 0.035) * (1 - (1 + 0.035)^8)

= 218,70

15.

Coupon bond - Flervalsfråga

Suppose a bond with maturity in 7 years and semi-annual coupons has a face value equal to 1000. Its coupon rate is 8% and it has a yield-to-maturity (YTM) equal 12% (expressed as an APR with semi-annual compounding).

Step 1: Data

Maturity: 7

FV: 1000

CPN rate: 0,08

YTM1: 0,12

N: 14

YTM1 är den givna räntan, vi behöver dock justera den till semi-annual coupons. Det går ju två halvår på ett år och eftersom räntan är en APR kan vi bara dela den givna räntan, 12% på 2. Detta ger oss YTM2.

N blir då 14, eftersom det går två halvår på ett år,

7*2 =14

Step 2: CPN and YTM2

CPN:

FV * CPN rate / 2

YTM2:

YTM1 / 2

Step 3: Answer

= (CPN/YTM2) * (1 - (1/((1 + YTM2)^N)))

+ (FV/((1 + YTM2)^N)

Or

Provided info:

Maturity: 7 years

Semiannual coupons: face value: 1000 SEK

Coupon rate: 0,08%

YTM (expressed APR, semiannual compounding): 0,12%

Semiannual coupon payment: 40

Number of periods: 14

Semiannual YTM: 0,06

Bond price: ?

Calculate: (1+0,06)^14 = 2,260903956

Calculate: 1 / (1+0,06)^14 = 0,4423009644

Calculate: 40 * (1 - 0,4423) / 0,06 = 371,7993571

Calculate the PV of the face value: 442,3009644

Add the PV:s of the coupons and the face value: 814,1003215

Answer: 814,1003215

16. Mortgage payments - Flervalsfråga

You would like to purchase a car whose price is 237,000 SEK. You are offered a loan to cover the entire amount and its terms establish an APR with monthly compounding equal to 6%. The loan is supposed to be paid back in 10 years with equal monthly payments.

What is the monthly payment? (Answers rounded to the nearest whole number).

To calculate the monthly payment for a loan, we can use the formula for the present value of an annuity.

The formula is as follows:

Monthly Payment = PV * r / (1 - (1 + r)^(-n))

PV = is the present value or loan amount

r = is the monthly interest rate n is the total number of payments

Given the information provided:

Loan amount (PV) = 237,000 SEK

Annual Percentage Rate (APR) = 6%

Loan term (n) = 10 years

Monthly compounding (12 periods per year)

Step 1: Calculate the monthly interest rate

Monthly interest rate = (1 + APR)^(1/12) - 1

Monthly interest rate = (1 + 0.06)^(1/12) - 1

Monthly interest rate = 0.004867

Step 2: Calculate the monthly payment

Monthly Payment = 237,000 * 0.004867 / (1 - (1 + 0.004867)^(-10*12))

Answer: After performing the calculation, the monthly payment for the loan is approximately 2631 SEK. Therefore, the correct answer is 2631 SEK.

17. Options - Flervalsfråga

You own 1 put options with strike-price equal to 70 and 2 call options with strike-price equal to 50. They both have the same maturity and the same underlying stock whose current price is 100. What will be the total payoff of your options at maturity if the price of the stock at that point is equal to 62?

To calculate the total payoff of your options at maturity, we need to consider the payoff of each individual option and then sum them up.

Stock price at maturity - Strike price = Call option payoff

Call option payoff: 62 - 50 = 12

 Put option payoff: 70 - 62 = 8 

To calculate the total payoff, we sum up the payoffs of the put option and the call options:

Put option payoff + Call option payoff + Call option payoff = Total payoff

8 + 12 + 12 = 32 = Total payoff 

Therefore, the correct answer is 32.

18. Expected return of a portfolio - Flervalsfråga

Expected return of a portfolio

Suppose that in one year only three possible outcomes can take place. In each one of those possible scenarios the return of the stock of the companies Spin and Bang will take the following values with the indicated probabilities:

(Probabilities) Spin Bang

(0.2)            0.09        0.15        

(0.3)  -0.07    0.10

(0.5)  0.37      0.12

Suppose that you would like to invest in a portfolio of the two and your investment wealth is equal to 100,000 SEK. You would like to allocate 35,000 SEK to Spin and the rest will be invested in Bang.

What will be the expected return of your portfolio? (Answers rounded to two decimal digits)

To calculate the expected return of the portfolio, we need to follow these steps:

1. Calculate the expected return for each stock (Spin and Bang).

2. Determine the weights of each stock in the portfolio.

3. Compute the expected return of the portfolio using the weighted average of the expected returns of the individual stocks.

Step 1: Calculate the Expected Return for Each Stock

The expected return (E(R)) of a stock is calculated as follows:

E(R) = ∑(Probability * Return)

Expected Return for Spin

(E(R) Spin) = (0.2 * 0.09) + (0.3 * -0.07) + (0.5 * 0.37

(E(R)Spin) = (0.018) + (-0.021) + (0.185)

(E(R)Spin) = 0.018 - 0.021 + 0.185

(E(R)Spin) = 0.182

Expected Return for Bang

(E(R) Bang) = (0.2 * 0.15) + (0.3 * 0.10) + (0.5 * 0.12

(E(R) Bang) = (0.03) + (0.03) + (0.06)

(E(R) Bang) = 0.03 + 0.03 + 0.06 = 0.12

(E(R) Bang) = 0.12

Step 2: Determine the Weights of Each Stock in the Portfolio

Total investment = 100,000 SEK

Investment in Spin = 35,000 SEK

Investment in Bang = 100,000 - 35,000 = 65,000 SEK

The weights are calculated as follows:

W_Spin = 35,000 / 100,000 = 0.35

W_Bang = 65,000 / 100,000 = 0.65

Step 3: Compute the Expected Return of the Portfolio

The expected return of the portfolio (E(R)Portfolio) is calculated as:

(E(R) Portfolio) = (W_Spin * (E(R) Spin) + (W_Bang * E(R)Bang)

E(R) Portfolio = (0.35 * 0.182) + (0.65 * 0.12)

(E(R_Portfolio) = 0.0637 + 0.078

E(R_Portfolio) = 0.1417

14,17%

19. Portfolio Theory - (ej klar)

A portfolio has two elements: stock A and stock B. The weight on stock A is equal 0.2. The correlation between the return of stock A and B is 0.7. The table below shows (possibly relevant) additional information. The variance for each stock was computed by using rates of returns and not percentages. What is the expected return of the portfolio? What is its standard deviation? (Round your answer to two decimal digits)

Stocks:     Expected return:     Variance:

A:                     15%           0.0227

B:                11%                0.0123

20. Beta of a portfolio

Suppose you hold a portfolio of the market portfolio and the risk-free asset. Your portfolio weight on the risk-free asset is equal to -0.5.

What is the Beta of your portfolio?

Alright, let’s break it down simply!

Imagine you have two types of toys: one is a super bouncy ball (the market portfolio) and the other is a squishy teddy bear (the risk-free asset). 

1. **Bouncy Ball (Market Portfolio):** This toy’s bounce is like the market’s ups and downs. It has a Beta of 1.0, meaning it moves with the market.

2. **Squishy Teddy Bear (Risk-Free Asset):** This teddy bear is super calm and doesn’t bounce at all, so it has a Beta of 0.0. It doesn’t move with the market at all.

Now, if you have a toy box where you mix these toys, the Beta of your toy box depends on how many of each toy you have.

In your case:

- You have a weight of -0.5 for the teddy bear. This means you actually owe half a teddy bear (or you’re borrowing it) and holding 0.5 of its value.

- You have a weight of 1.5 for the bouncy ball. This is because, with the negative weight of the teddy bear, you’re actually holding more of the bouncy ball to balance things out.

To find the Beta of your toy box (portfolio):

- Multiply the Beta of each toy by its weight.

- Add these numbers together.

For your portfolio:

- The bouncy ball (market portfolio) Beta is 1.0, and you have a weight of 1.5. So, \(1.0 \times 1.5 = 1.5\).

- The teddy bear (risk-free asset) Beta is 0.0, and you have a weight of -0.5. So, \(0.0 \times -0.5 = 0.0\).

Adding these together:

(1.5 + 0.0 = 1.5)

So the Beta of your portfolio is indeed 1.5! This means your toy box (portfolio) moves 1.5 times as much as the market.

Answer: 1.5