Question

Calculate the stock’s expected return, variance and standard deviation. Explain the meaning of expected return, variance, and standard deviation. What do your answers actually mean?

demand for the company's products	probability of this demand occuring	rate of return if this demand occurs
weak	0.15	(30%)
below average	0.20	(3%)
average	0.35	18%
above average	0.20	25%
strong	0.10	31%

You finally purchased a house 3 years ago. The price tag on your house was $160,000. You were able to secure a 15-year mortgage at 8.5%, monthly compounding. Currently, what is the remaining balance on your mortgage?

3. It is time to buy a used Toyota Camry. You got a loan for 10 years. The car cost you $12,000. It is not a new car but in very decent shape. The bank expects you to pay $150 a month. Calculate the EAR.

4. After negotiations, you purchased a 20-year investment that pays you $100 at the end of year one, $500 at the end of year 2, and $750 at the end of year 3. Additionally, the investment pays you some fixed cash flow, let’s call it “X”, at the end of each of the remaining seventeen years. You pay $5,544.87 for this investment. The required return on similar investments is 9%. Calculate the annual cash flow that you are going to receive at the end of the final seventeen years; in other words, find “X."

Answer 1

1
Expected return=0.15*(-30%)+0.20*(-3%)+0.35*18%+0.20*25%+0.10*31%=9.300%

Standard Deviation=sqrt(0.15*(-30%-9.3%)^2+0.20*(-3%-9.3%)^2+0.35*(18%-9.3%)^2+0.20*(25%-9.3%)^2+0.10*(31%-9.3%)^2)=19.617%

Variance=19.617%^2=0.038482669

2
=FV(8.5%/12,12*3,-PMT(8.5%/12,12*15,160000),-160000)=141937.335691292

3
=(1+RATE(10*12,-150,12000))^12-1=9.04376809963556%

4
=(5544.87-100/1.09-500/1.09^2-750/1.09^3)*1.09^3*0.09/(1-1/1.09^17)=675.000734694479