I've been avoiding revising these type of questions as i just don't know where to start so any hints or tips would be appreciated if not necessarily the full blown answer, thank you!!
Here's the question :
A portfolio has two assets, Asset 1 and Asset 2. The returns on these assets are given by R1 and R2 respectively where:
R1 ~ N(1.5,1)
R2 ~ N(1.5,2)
The returns on the assets are independent of one another.
a) Which asset is riskier? Explain your reasoning.
b) What is the probability that the first asset yields a negative return?
c) What is the probability that the second asset yields a negative return?
d) An investor is choosing between Portfolio A (all Asset 1), Portfolio B (invest half your funds in Asset 1 and half of Asset 2) and Portfolio C (all Asset 2). The investor has 100 units to invest. Calculate the expected return and variance for each portfolio.
e) Discuss your recommendations to the investor based on your results from d).
This is a stochastic dominance question. The riskier of the two is the one with the higher standard deviation, in this case, R2.
To determine the chance of getting a negative return, look how far away 0 is from the mean and how many standard deviations that is. Then look at your chart and figure out how much of the bell curve lies bellow 0.
For R1, we dont need to even convert since sigma is 1. 0 is 1.5sigma away, therefore, it will have a negative return approximately 1-0.9332=0.0668 or 6.68% of the time.
For R2, we calculate z score . Our calculated z-score is -0.75. Z scores are always positive, so it is 0.75. On a table, 0.7734 of the data falls to the left of that but we want to flip it (it is symetrical) so 1-0.7734=0.2266 or 22.66% of the data lies to the left of 0 ( would have a negative return 22.66% of the time.
lol i read december <_<
Hope this starts you along