# I could use some help with this one please

An financial analyst is in the process of measuring the annualized return of an investment portfolio. Consider the following information: t0: purchase an initial 1 share of Microscam for \$65.40 t1: purchase an additional 1 share of Microscam for \$68.12 t1: receive a dividend of \$0.75 t2: purchase an additional 1 share of Microscam for \$75.95 t2: receive a dividend of \$0.77 t3: sell 3 shares for \$82.76 per share Assuming no taxes or transaction costs, that dividends are not reinvested, and that each period represents one year, what is the time-weighted rate of return per year on this portfolio? A. 8.27% per year B. 10.73% per year C. 14.43% per year D. 8.92% per year thanks in advance

That must be D.

that is correct but can u explain ? I keep getting irrelevant answers at the end

In year 0 you get a capital gain of 68.12-65.40=2.72 and a dividend of 0.75, that would give you a HPY0 of 5.3058% In year 1 you get a capital gain of 75.95-68.12=7.83 and a dividend of 0.77 that would give you a HPY1 of 12.6248% In year 2 you get a capital gain of 82.76-75.95 = 6.81 that would give you a HPY2 of 8.9664% Time weighted is the geometric mean = [(1+HPY0)*(1+HPY1)*(1+HPY2)]^(1/3)-1, that gives you 8.9246 (more or less).

If you would turn around to sell the share at the end of year 0 (or both at the end of year 1), probably you will not get the 68.12, 75.95 respectivelly in the real world, but for the purposes of this problem, it is safe to assume so. There is no need to consider the fact that you have bought a second share and a third one, or that you received 2 dividends in year 2. It is irrelevant for the time weighted, but it would be necessary to know and introduce it in the cash flow when you calculate the dollar weighted return.

ok my mistake (again) … thanks

Better learn from mistakes now than later Thanks, great review