1.
a) “The standard deviation of a portfolio's return cannot be reduced to zero by holding all the securities in the market.” True or false? Explain. (2 mark)
An investor buys 1 share of ABC Ltd at the price of $32 on December 1, 2019. The firm is not expected to pay any dividends. Consider the following three possible scenarios for the share price on December 1, 2020:
· $50 with a probability of 30%
· $35 with a probability of 60%
· $23 with a probability of 10%
) Calculate the expected return for holding the share for a year. (2 mark)
c) Calculate the variance of return and standard deviation of return. (2 marks)
d) On December 1, 2020, the share is worth $36 and the investor just received a dividend of $2.50. Calculate the total holding period return and capital gains return over the one-year period. (2 marks)
e) Explain the difference between expected return and realised return. (2 marks)
QUESTION END
Question 2.
a) Explain the relationship between the yield to maturity of a premium bond and its coupon rate. (2 marks)
) ABC Ltd issues two different bonds with the same yield to maturity:
· a 20-year zero coupon bond
· a 15-year semi-annual coupon bond
Explain which bond is subject to less interest rate risk. (2 marks)
c) ABC Ltd is planning to issue 16-year semi-annual coupon bonds with a face value of $1,000 and a coupon rate of 6.5%. The nominal yield to maturity of potential investors is estimated to be 7.6% per annum. Calculate the required number (expressed as an integer) of semi-annual coupon bonds to be issued if the firm aims to raise $15 million. (3 marks)
d) You purchase a bond issued by XYZ Ltd, which is a 9% semi-annual coupon bond with a term to maturity of 12 years, and cu
ently trading at par. 3 years later, immediately after receiving the 6th coupon payment, you sell the bond to your best friend. You best friend’s nominal yield to maturity is 7% per annum. Write down an equation that can be solved to find your total realised return over the 3-year holding period. (3 marks)
Question 3.
· Option 1: You will deposit $600 at the end of each month for the next 20 years. The nominal interest rate is 12% per annum compounded monthly.
a) Calculate the future value of your savings immediately after the last deposit. (1 mark)
) To help you, your parents will deposit a bonus of $1100 into your savings account at the end of every 5 years, in additional to your deposits in part a). Calculate the future value of your savings immediately after the last deposit. (2 marks)
· Option 2: This savings plan requires you to make your first deposit immediately. You will make regular quarterly deposits for the next 20 years. Your savings goal for retirement is $500,000 (at the end of the 20 years). The effective annual rate is 12%.
c) Calculate the effective quarterly interest rate. (1 mark)
d) Calculate the size of the required quarterly deposit. (2 marks)
· Option 3: You will make regular deposits for the next 20 years. Specifically, you will make regular semi-annual deposits of $6,000 for the next 15 years. Then you will stop saving for a year. After that, you will make regular deposits of $10,000 every 2 years for the remaining 4 years. The first deposit is made 6 months from now. The effective annual rate for the first 16 years (starting today) is 10% and the nominal interest rate in subsequent years is 6% per annum compounded daily.
e) Calculate the future value of your savings immediately after the last deposit. (3 marks)
f) How many deposits it will take for the balance to first exceed $130,000? (1 mark)
1.
a) “The standard deviation of a portfolio's return cannot be reduced to zero by holding all the securities in the market.” True or false? Explain. (2 mark)
An investor buys 1 share of ABC Ltd at the price of $32 on December 1, 2019. The firm is not expected to pay any dividends. Consider the following three possible scenarios for the share price on December 1, 2020:
· $50 with a probability of 30%
· $35 with a probability of 60%
· $23 with a probability of 10%
) Calculate the expected return for holding the share for a year. (2 mark)
c) Calculate the variance of return and standard deviation of return. (2 marks)
d) On December 1, 2020, the share is worth $36 and the investor just received a dividend of $2.50. Calculate the total holding period return and capital gains return over the one-year period. (2 marks)
e) Explain the difference between expected return and realised return. (2 marks)
QUESTION END
Question 2.
a) Explain the relationship between the yield to maturity of a premium bond and its coupon rate. (2 marks)
) ABC Ltd issues two different bonds with the same yield to maturity:
· a 20-year zero coupon bond
· a 15-year semi-annual coupon bond
Explain which bond is subject to less interest rate risk. (2 marks)
c) ABC Ltd is planning to issue 16-year semi-annual coupon bonds with a face value of $1,000 and a coupon rate of 6.5%. The nominal yield to maturity of potential investors is estimated to be 7.6% per annum. Calculate the required number (expressed as an integer) of semi-annual coupon bonds to be issued if the firm aims to raise $15 million. (3 marks)
d) You purchase a bond issued by XYZ Ltd, which is a 9% semi-annual coupon bond with a term to maturity of 12 years, and cu
ently trading at par. 3 years later, immediately after receiving the 6th coupon payment, you sell the bond to your best friend. You best friend’s nominal yield to maturity is 7% per annum. Write down an equation that can be solved to find your total realised return over the 3-year holding period. (3 marks)
Question 3.
· Option 1: You will deposit $600 at the end of each month for the next 20 years. The nominal interest rate is 12% per annum compounded monthly.
a) Calculate the future value of your savings immediately after the last deposit. (1 mark)
) To help you, your parents will deposit a bonus of $1100 into your savings account at the end of every 5 years, in additional to your deposits in part a). Calculate the future value of your savings immediately after the last deposit. (2 marks)
· Option 2: This savings plan requires you to make your first deposit immediately. You will make regular quarterly deposits for the next 20 years. Your savings goal for retirement is $500,000 (at the end of the 20 years). The effective annual rate is 12%.
c) Calculate the effective quarterly interest rate. (1 mark)
d) Calculate the size of the required quarterly deposit. (2 marks)
· Option 3: You will make regular deposits for the next 20 years. Specifically, you will make regular semi-annual deposits of $6,000 for the next 15 years. Then you will stop saving for a year. After that, you will make regular deposits of $10,000 every 2 years for the remaining 4 years. The first deposit is made 6 months from now. The effective annual rate for the first 16 years (starting today) is 10% and the nominal interest rate in subsequent years is 6% per annum compounded daily.
e) Calculate the future value of your savings immediately after the last deposit. (3 marks)
f) How many deposits it will take for the balance to first exceed $130,000? (1 mark)