NPI Formula Change. Jeff Fisher Joe D Alessandro

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1 NPI Formula Change Jeff Fisher Joe D Alessandro?

2 Unintended Consequences of the Freeze

3 The higher the percentage of sold properties in a quarter, the more the NPI is overstated. For every 100 basis point increase in percent sold the NPI is overstated by 125 basis points.

4 The overstatement is not as much for ODCE only properties because they are revalued more frequently so no appraisal lag in the gain for the sale quarter. The return is now overstated by about 27 basis points for each 100 basis point increase in the percent sold.

5 Questions we Pondered Why do we do use Modified Dietz to estimate an IRR for a quarter when we then chain link them to get a time weighted return (TWR)? When is it better to carve up a period (e.g., quarter) into smaller periods (e.g., months or uneven periods) that are linked to get a TWR? Is the sold property bias we observe due to using Modified Dietz to estimate an IRR? Or is it due to using an IRR for a quarter rather than breaking up the quarter into sub periods? How much does the gain in a sale quarter need to be overstated to make up for the understated returns prior quarters due to appraisal lag?

6 Review of Modified Dietz Modified Dietz (MD) is used to approximate an IRR for a period when there are interim cash flows between valuations. When used in conjunction with calculation of time weighted returns (TWR), it was intended as a way to get a return where there are relatively small intra-period cash flows and it isn t feasible to have a valuation at the time of the cash flow. A time weighted return (TWR) chain links the periodic IRRs (estimated with Modified Dietz). Modified Dietz becomes a poor approximation of an IRR when there is a large intraperiod cash flow. As of 2010 for stocks and bonds, GIPS requires a valuation whenever there is a large cash flow. The return for this sub-period would then be chain linked as part of a TWR Periods can be uneven This neutralizes the impact of a change in the amount of capital invested.

7 NPI Formula The NPI formula is derived from MD assuming partial sales occur mid quarter. After the freeze full sales were treated as a partial sale It is designed to calculate a quarterly return when there are intra-period cash flows. The IRR is impacted by the timing of the cash flows within the quarter. For many cuts of the data, the partial sales result in a large intra-period cash flow. Sale prices are obviously an indication of value

8 Comparison of IRR, NPI (Dietz) and Intra-Quarter TWR Sold Prop 1 Prop 2 Portfolio relative size of sold property 100% time zero half a qtr full qtr NPI/MD 3.00% % 33.08% half IRR 1.49% 40.00% 14.84% qtr IRR 3.00% 31.89% Half Qtr Prop 1 Value Prop 2 Value st half Value nd half Value TWR 20.50% 1.98% 22.89% The TWR weighs the two periods within the quarter equally whereas the IRR puts more weight on the first (sale) period with the high return due to appraisal lag. IRR 31.89% NPI 33.08% TWR 22.89%

9 Return Comparisons as % of Sold Properties Increases Modified Dietz vs true IRR IRR vs Intraperiod TWR

10 Based on Sold Properties from * 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Closed End Funds Sale Price vs App Value % 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% ODCE Sale Price vs App Value % 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Non-ODCE Open End Sale Price vs App Value % 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Separate Account Sale Price vs App Value *Started at 10% difference between sale price and appraised value.

11 New Approach Deals Property with Catchup from Appraisal Lag Half Quarter Actual Market Values Prop 1 Market Value Prop 2 Market Value Assuming no appraisal lag. BMV EMV Return New Return NPI % % 4.00% % % 3.87% Since inception 3.92% 3.94% Half Quarter Lagged Appraised Values Prop 1 Market Value Prop 2 Market Value Sold property needs to catch up in value change from appraisal lag. BMV EMV Return New Return NPI % % 2.00% % % 6.62% Since inception 3.92% 4.29% NPI formula overstates when appraisal lag.

12 Conclusions Ideally a return should be calculated up to the time when sales are taking place. Sales are a large cash flow. As noted previously for stocks and bonds there should be a valuation when there is a large cash flow. It isn t feasible to do this as of the exact date of each sale. But it is feasible to do monthly with sales assumed to occur at the end of the month. An interpolation of the monthly value of unsold properties combined with the actual prices of sold properties is a reasonable intra-period value estimate. This value pattern doesn t differ significantly from that implied by the IRR Although not a true valuation of every property it is consistent with GIPs intent to neutralize the impact of large sales in returns. Better to have an interpolated value estimate than the bias due to the large cash flow from sold properties.