Fact Pattern:

You are currently working as a portfolio analyst with a local investment management firm. One of

your functions is to prepare summaries of portfolio performance for the firm's clients. This

performance analysis includes not only returns achieved, but comparisons with the market and

measures of risk exposure. One of the portfolios you are asked to analyze is called the Greshak

Portfolio. Based on your research, the following information was collected for the prior six $(6)$ years:

Further analysis indicated that the share price of the Greshak Portfolio was $$20\mathrm{.}00$ at the outset of

the measurement period $($i$.$e$.,$ the beginning of Year $1).$

Required:

Based on the fact pattern above, answer the following questions:

Define a time$-$weighted rate of return and a dollar weighted rate of return in a portfolio

performance context. Compare and contrast the two measures of performance.

What was Greshak Portfolio's time$-$weighted compound annual rate of return over the six year

period provided? What was the comparable rate of return on the market, as measured by the

S&P $500,$ over that same period time?

a$.$ How did the return on the portfolio compare to the market return over the period

analyzed?

b$.$ Did the portfolio bear more or less systematic risk than the market? Explain.

c$.$ Were the returns earned by portfolio more or less variable than the market returns?

Explain.

d$.$ Based on your answers above, can you conclude that Greshak's Portfolio was more or

less risky than the overall market? Support your answer.

What was Greshak Portfolio's dollar$-$weighted compound annual rate of return over the six

year period provided?

If the Greshak Portfolio had $500$ shares outstanding at the beginning of the first year of the

analysis period, how much would the entire Portfolio be worth at the end of the six year

period? For purposes of this analysis, assume that all dividends were reinvested in the

Portfolio in the year received at year$-$end values. What was the Portfolio's compound annual

growth rate over the six year period analyzed?

Why are the rates of return determined in Questions #$2,$ #$3$ and #$4$ above different? Explain.

Using the original data given in the case study $($including the beginning balance of $500$ shares

worth $$20\mathrm{.}00$ each$),$ now assume that Greshak adds an additional $$2,000$ at the beginning of

each year to the portfolio. What would the value of the portfolio be at the end of the six year

period using both a time$-$weighted and a dollar$-$weighted calculation method? Assume all

dividends were reinvested in the Portfolio in the year received at year$-$end values. How do

these return metrics compare to the returns calculated above? Explain.