Question

1. The table below is the YTM of U.S. Treasuries with different maturities on April 1, 2020.

1 yr.	2 yr.	3 yr.	5 yr.	7 yr.
0.16%	0.23%	0.28%	0.37%	0.51%

1. What is the expected two-year rate in three years according to the Pure Expectations Theory?                                                    
2. What is an inverted yield curve? Give one reason that may cause the yield curve to invert.                                                                 

2. Johnny's portfolio consists of $100,000 invested in stock X which has a beta of 0.8, $150,000 invested in stock Y which has a beta of 1.2, and $50,000 invested in stock Z which has a beta of 1.8.   What is the portfolio beta according to CAPM?

3. Silky Smooth Studio (SMS) is considering investing in a movie project. The expected cash flows of the project are given in the table below.

Year	0	1	2	3
Cash Flow	-$100,000	$45,000	$45,000	$45,000

       

The required return of the project is 12 percent.

1. Using Net Present Value as the decision criterion, should SMS invest in this movie? Explain carefully.                                                   
2. What is the discounted payback period of this project?                   

4. “In general, the larger a portfolio (in terms of number of assets) the lower its non-systematic risk.”
   1. Define systematic risk and non-systematic risk, and briefly explain their difference.                                                                    
   2. Do you agree or disagree with the above statement? Justify your answer.                                                                                

5. Efficient Market Hypothesis
   1. Describe in 100 words or less what it means when we say the capital market is efficient and outline its implications.                              
   2. If the capital market is efficient, does it mean you can expect to do well as the market by randomly picking stocks to form a portfolio? Explain why or why not.                                                                       

Answer 1

Solution:

a) The Expected two year rate in three years is as follows.

The relation between spot and forward rates is given by following equation:

Ft-2,t  = [(1+ St)^t / (1+St-2)^t-2]^1/2 - 1

F3,5 = [(1.0037) ^ 5 / (1.0028)^ 3 ] ^ 1/2 - 1

=  (1.0186 / 1.0084) ^ 0.5 - 1

= 1.0051 - 1

= 0.0051 i.e 0.51%

b) Inverted yield curve represents a situation in which long term debt instruments have lower yield than short term debt instruments which has more or less same characteristics & quality.

The reason for inverted curve is more demand for long term bonds which lowers the yield on bond .

Calculation of portfolio beta according to CAPM is as follows

Beta of porfolio =( $ 100000 * 0.8 + $ 150000 * 1.2 + $ 50000 * 1.8) / $ 300000

= 350,000 / 300,000

= 0.857 i.e 0.86

Silk Smooth Studio (SMS)

a) Net present value = Present value of inflows - Present value of outflows

= $ 45,000 * PVAF (12%, 3) - $ 100,000

= $ 1,08,082.41 - $ 100,000

= $ 8,082.41

As NPV is Positive SMS Should invest in this movie.

b) Discounted payback period

Years	Discounted cash flows	Cumulative cash flows
1	45000 / 1.12 = 40178.57	40178.57
2	45000 / (1.12)^2 = 35873.72	76052.3
3	45000 / (1.12)^3 = 32033.11	108082.4

As Initial outflow of $ 100,000 is recovered in 3rd year

i.e 32033.11 / 12 = 2669.18 per month

we require (100,000 - 76,052.3) = $ 23,947.70 in 3rd year

so , 23,947.7 / 2669.18

= 8.97 months

therefore payback period is 2 years & 8.97 months.

a) Systematic risk is the risk associated with the entire market or segment which is not specific to particular stock.

whereas non-systematic risk is associated with a specific industry , segment ehich can be elminated through diversification of portfolio.

b) I dont agree with the above statement that the larger the number of asets in a portfolio , the lower its unsystematic risk because it depends on whether the stocks in a portfolio are invested in different industries or not.

if they are invested in same industry then there will be more unsystematic risk.