As a national provident fund in Malaysia, the Employees Provident Fund s (EPF) primary investment objective is to seek a balance between profitability and prudence. Key considerations in investment decisions include the criteria of safety, stability, liquidity, and risk-adjusted returns. In order to meet its investment obligations, the EPF adheres to a disciplined investment procedure and guidelines laid out in the EPF Act(Malaysia) 1991. Suppose, over the years, you ( as an employee) have invested in the Employees Provident Fund (EPF) which has been registering an annual return that is approximately normally distributed with a mean (expected value) return of 5.8% and standard deviation 3.5%.

(a) Find the probability that your annual return from this fund will be negative?

(b) Suppose you have an option to continue investing in this fund next year only if the annual return exceeds 5%. Find the probability that you will invest in this fund next year?

(c) If the EPF managers decide to modify the composition of the funds portfolio, they can potentially raise its mean annual return to 7%. However, this will also raise the standard deviation of returns to 5%. You are required to recalculate parts (a) and (b) in light of this decision. State any assumptions you are making.

(d) Would you continue to invest in this fund if the managers decide to modify the composition of the funds portfolio as suggested in part (c)? Explain your decision.

(e) State the characteristics of a normal distribution and explain the need to convert a random normal variable to a standardized form.