As an investment advisor for MREAF $($Momentum Real Estate Advisory Fund$),$ you are about to make a presentation to the portfolio manager of the ET&T pension fund. You would like to show what would have happened had ET&T made an investment in MREAF during the past $13$ quarters. The ET&T manager has provided you with historical data on the performance of its portfolio, which is made up entirely of common stock. Historical data for the ET&T portfolio and MREAF are as follows:

Period Ending ET&T Common Stock Fund MREAF Real Estate Fund

Unit Value Quarterly Dividend Unit Value Quarterly Dividend

Quarter $1$ $ $701\mathrm{.}00$ $ $8\mathrm{.}28$ $ $70\mathrm{.}00$ $ $2\mathrm{.}17$

Quarter $2752\mathrm{.}508\mathrm{.}1180\mathrm{.}052\mathrm{.}14$

Quarter $3850\mathrm{.}5210\mathrm{.}3090\mathrm{.}802\mathrm{.}01$

Quarter $4953\mathrm{.}759\mathrm{.}81100\mathrm{.}502\mathrm{.}01$

Quarter $51,047\mathrm{.}5712\mathrm{.}0599\mathrm{.}141\mathrm{.}87$

Quarter $61,221\mathrm{.}7014\mathrm{.}1795\mathrm{.}501\mathrm{.}81$

Quarter $71,443\mathrm{.}9017\mathrm{.}1893\mathrm{.}771\mathrm{.}79$

Quarter $81,263\mathrm{.}3114\mathrm{.}9180\mathrm{.}311\mathrm{.}54$

Quarter $91,258\mathrm{.}5613\mathrm{.}8477\mathrm{.}341\mathrm{.}49$

Quarter $101,526\mathrm{.}7218\mathrm{.}3276\mathrm{.}531\mathrm{.}44$

Quarter $111,616\mathrm{.}8119\mathrm{.}7378\mathrm{.}421\mathrm{.}51$

Quarter $121,624\mathrm{.}0819\mathrm{.}9879\mathrm{.}011\mathrm{.}53$

Quarter $131,560\mathrm{.}2518\mathrm{.}8881\mathrm{.}751\mathrm{.}55$

Required:

a$.$ Calculate the quarterly HPR for each investment. HINT: The first HPR will be in quarter $2$ because $2$ quarters are needed to calculate a return. The first quarter dividend won$$t be included in the calculations.

b$.$ Calculate the arithmetic mean HPR$,$ the standard deviation of the HPRs$,$ and the geometric mean for each fund. Which fund contained more risk per unit of return?

c$.$ Calculate the covariance and correlation between Stock Fund and Real Estate Fund?

d$.$ Would the proposed portfolio provide any investment diversification?