Consider the following annual period-by-period returns for an "open-ended" commingled real estate fund (CREF), an investment vehicle for institutional investors. Investors can put capital into, and withdraw capital out, of this type of fund on the basis of the appraised value of the assets in the fund, which are regularly and frequently reappraised. Investors purchase "units" in the fund in the same way you and I buy units of open-ended stock or bond mutual funds.

Unit Value Income Paid
at end of yr. out per unit (end of year)
2009: $100 -
2010: 115 $5.00
2011: 122 6.00
2012: 110 5.50

(a) Determine the annual total holding period (period-by-period) returns for the fund each of the three years 2010, 2011 and 2012 [Help: for the 2010 return the starting value is $100 and ending value is $115 while the fund also returned $5 in income - use this to figure out the total one year holding period return as appreciation plus income yield]

(b) Based on the period-by-period returns you calculated above, evaluate both the arithmetic and geometric (compound) average annual total returns for the 2010-12 period?

(c) Now consider the investment performance of a pension fund that purchased two "units" of the CREF at the end of 2010 and one more "unit" at the end of 2011. The pension fund liquidated its position in the CREF at the end of 2012. Calculate the pension fund's IRR on this investment and describe how and why it differs from the average (mean) period-by-period return to the fund over the 2010-2012 period?