This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
NCREIF TWR Denominator Issues
One is Big, One is Small !
by Dean Altshuler, PhD, CFA
Bard Consulting LLC
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
- --
Denominator Issue #1 – Before and After Fee Denominators Are Frequently Understated, Causing Overstated TWRs
Compared to ODCE
1. Purpose of TWRs – Measure Manager’s Skill On a Unitized Basis, Not Investor’s Rate of Return (“ROR”)
a. “TWR is the manager’s rate of return, IRR is the investor’s ” – many sources
b. “Each manager should be judged on the return he received per dollar invested in the fund” – Peter Dietz
2. Meaning of After Fee TWR – Manager Skill, Adjusted for the Cost of Employing Them
a. Could select managers based on comparing their track record of after fee TWRs, but what if the more
skilled, more costly, manager will negotiate on fees? Before and after fee rates of return both matter!
3. What is known as “True TWR”, which is easy and cheap to compute with publicly traded stocks, is the gold
standard. See Exhibit 1 for a simple example of how true TWR is computed and how conclusions made
from comparing TWRs are often different from those based on comparing profits or IRRs.
a. Due to the cost and time involved in valuing real estate, the industry uses approximations such as fixed
quarterly periods and Modified Dietz rates of return. However, thinking about True TWR better
informs the reader as to the intent of TWR. Which is that, each time period, whether of variable length
between successive cash flows (True TWR) or of fixed length between valuation dates (linked MD rates of
return) is intended to be completely independent of that of its ‘neighbors’, and that a longer term
cumulative TWR is merely an accumulation (or average if you prefer to annualize them) of those
independent ‘unitized’ rates of return. As such, each rate of return is as important as the other,
irrespective of the comparative amounts of money invested in each period, and there is no connection
between the rate of return of one period and the rate of return of the prior period.
2
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
EXHIBIT 1: SIMPLE THREE PERIOD ILLUSTRATION OF HOW RATES OF RETURN ARE COMBINED WITH TRUE TWR
True TWR
Manager #1
Beginning of Period #1 NAV
End of Period #1 NAV
Contribution made at End of Period #1
Beginning of Period #2 NAV
End of Period #2 NAV
Contribution made at End of Period #2
Beginning of Period #2 NAV
End of Period #2 NAV
$100
$103
$500
$603
$633
$100
$733
$740
Period #1 ROR
Period #2 ROR
Period #3 ROR
IRR **
3.0%
5.0%
1.0%
Cumulative TWR 9.2%
True TWR
Manager #2
Beginning of Period #1 NAV
End of Period #1 NAV
Contribution made at End of Period #1
Beginning of Period #2 NAV
End of Period #2 NAV
Contribution made at End of Period #2
Beginning of Period #2 NAV
End of Period #2 NAV
$100
$103
$100
$203
$213
$500
$713
$727
Period #1 ROR
Period #2 ROR
Period #3 ROR
Period #0 Cash Flow
Period #1 Cash Flow
Period #2 Cash Flow
Period #3 Cash Flow
Per Period IRR
-$100
-$500
-$100
$740
2.8%
Whole Dollar Profit
$40
Cumulative IRR
8.8%
IRR **
3.0%
5.0%
2.0%
Cumulative TWR 10.3%
Period #0 Cash Flow
Period #1 Cash Flow
Period #2 Cash Flow
Period #3 Cash Flow
Per Period IRR
-$100
-$100
-$500
$727
2.7%
Whole Dollar Profit
$27
Cumulative IRR
8.4%
**Assuming equal length periods
Moral of the Story: TWR is, in no way, intended to represent the increase in investor wealth. All it is intended to tell us is, over a cumulative term, is
which manager produced higher annualized 'unitized' rates of return. In this example, Manager #1 delivered a 9.2% cumulative TWR and Manager #2,
with a different cash flow experience (but who was also presumed to have had no control over the cash flows), delivered a 10.3% cum TWR; and, if so,
that Manager #2 is then deemed to be the "better manager" of the two. To wit, note that, in this example, the investor actually did better with
Manager #1 than with Manager #2, both in terms of IRR and profit. However, Manager #1 is deemed to have been lucky, in that he was given more
funds to invest just before the market was poised to have its best quarter. By design, TWR neutralizes all that and so, on a TWR basis, Manager #2
is shown to have delivered the superior cumulative TWR. In essence, it is assumed that, if Manager #2 had also been lucky enough to receive the
same $500 earlier to invest before the beginning of Period #2, his rate of return on $603 would have been the same 5% as what he produced on the
$203 he actually had and, hence, that he would have outperformed Manager #1 on an IRR and profit basis, given his outperformance in Period 3, i.e.,
in addition to having outperformed him on a TWR basis. This is what TWR is all about, a concatenation of unitized rates of return, one that neutralizes
the cash flows, so as to determine the better manager, rather than being about which manager delivered the greater wealth increase, or higher IRR.
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
- -Denominator Issue #1 (continued)
4. Issue #1 Is Using a Denominator That Is Reduced Based on Cumulative “Carried Interest” to Date
a. Large carried interest produces seriously distorted reflections of manager’s skill both before and after fee.
i. Causes quarterly RORs to be overstated in most cases (except when they are negative)
b. TWR is just a way to average the quarterly RORs, each as if independent of one another.
ii. If the quarterly RORs are wrong, then the TWR is wrong as well
c. Both before fee and after fee TWRs are distorted by Issue #1
5. History of Issue #1 – Inadvertently Introduced 10 Years Ago to Smooth the Impact of Incentive Fees That Are
Gradually Accruing
a. Went too far in modifying the quarterly MD ROR’s denominators in addition to the numerators
b. Forgot that TWR is the unitized manager’s ROR, not the investor’s money-weighted rate of return
c. The numerator adjustment works just fine by itself. It accounts for incremental fees each quarter,
ultimately accounting for all fees on a unitized rate of return basis.
6. Current Approach Often Produces Before Fee TWRs That Exceed the Return of the Portfolio!
7. Unlike Leverage, Accruing Carried Interest Is Not An Active Skill Decision of the Manager That We Want to
Assess. And If We Don’t Want to Assess Leverage, We’d Simply Compute Delevered TWRs, Such As What We Do
With The NPI Index.
3
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
Accrual Fee Calculation:
A Simple Example of Issue #1
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
Model Assumptions
• Quarterly Rates of Return: 20%, 2%
• Annual carried interest: $10 in the first
quarter, $0 in 2nd quarter
• Incentive fees are accrued and paid out
sometime later, at end of the fund’s life.
• For simplicity of illustration, this example
assumes all Period 1 gain is reinvested, and no
other fees are present.
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
Actual Portfolio TWR
Period 1 Period 2
Cumulative
Beginning Value
$100
$120
Gain
$20
$2.4
Ending Value
$120
$122.4
Portfolio’s Rate of Return
20%
2%
22.4%
Accrued Incentive Fee
$10
$0
$10
assumed reinvested
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
Current Return Methodology
• Period 2 denominators are reduced by cumulative carried interest.
• Before fee TWR should equal 22.4%, but doesn’t; it’s higher!
• Period 2 ROR overstates how mgr really did (2%), gross & net of fees.
Period 1 Period 2 Cumulative Total Return
After fee return
Numerator
$10
$2.4
Denominator
$100
$110
After fee return
10%
2.18%
12.4%
Before fee return
Numerator
$20
Denominator
$100
Before fee return 20%
$2.4
$110
2.18%
22.6%
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
Proposed Methodology
• Denominator for both after-fee and before-fee should reflect capital at work each qtr; 2nd qtr gross and net returns are the same since
the example assumes no additional fees are accrued in Period 2.
• Before fee cumulative return should equal 22.4% - and it does!
Period 1 Period 2 Cumulative Total Return
After fee return
Numerator
Denominator
After fee return
$10
$100
10%
$2.4
$120
2%
12.2%
Before fee return
Numerator
$20
Denominator
$100
Before fee return 20%
$2.4
$120
2%
22.4%
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
Conclusions
• Result is overstated before fee (aka gross) and after
fee (aka net) TWRs because denominators are too
low, due to subtracting carried interest that
represents capital at work.
• To ignore that capital is to overstate the manager’s
ability – in terms of how much in asset value it took
to earn the numerator’s net (and gross) gains.
• The overstatement builds dramatically as more and
more carried interest is accrued with more passing
quarters. Managers that do well early on will also be
rewarded with higher TWRs later on - survivorship bias!
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
- --
Denominator Issue #1 (continued)
8. Issue Impacts Only TWRs That Are Stated On a Before and After Fee Basis, Not the NPI.
a. Likely minimal impact on ODCE because few ODCE funds have incentive fees and fewer still likely accrue
carried interest for very long
b. Impacts funds, and indices created by NCREIF, that do accrue carried interest, making them appear
superior to ODCE (or ODCE plus premium), all else equal. Creates survivorship bias for quick starters!
9. (Admittedly) Extreme Scenario Produces Before Fee and After Fee TWR Annualized Errors of 3.0% and 2.4%,
Respectively, But There Are Surely Other Extreme Scenarios Out There With High Distortion
10. How to Get This Undone? Going Forward Only, Or Retroactively?
4
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
EXHIBIT 2 - SCENARIO: A CONSTANT 25% ANNUAL RETURN AND AN IRR HURDLE OF 12%
SIMPLE EXAMPLE: ASSUME AN APPRECIATING PORTFOLIO IS BOUGHT AND HELD TEN YEARS WITH THE INCENTIVE FEE PAYABLE ONLY AT THE END OF THE FUND
Portfolio's Annual Return
25%
Incentive Fee IRR Hurdle
12%
Promote Rate
FEE LOAD (TWR basis)
RESULTS (ANNUALIZED RATES OF RETURN)
A
Elapsed
Quarters
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
B
EOQ
Portfolio
NAV
$100.00
$105.74
$111.80
$118.22
$125.00
$132.17
$139.75
$147.77
$156.25
$165.21
$174.69
$184.72
$195.31
$206.52
$218.37
$230.89
$244.14
$258.15
$272.96
$288.62
$305.18
$322.68
$341.20
$360.77
$381.47
$403.36
$426.50
$450.96
$476.84
$504.19
$533.12
$563.71
$596.05
$630.24
$666.40
$704.63
$745.06
$787.80
$833.00
$880.79
$931.32
Current
Before
Fee TWR
28.00%
Proposed
Before
Fee TWR
25.00%
Before
Fee TWR
Overstatement
3.00%
Current
After
Fee TWR
22.74%
Before
Fee IRR
25.00%
C
Amount to
Reach
Hurdle
D
EOQ
Excess
Over Hurdle
E
F
G
Carried Interest
Balance @25%
Before Fee
Gain
After Fee
Gain
$102.87
$105.83
$108.87
$112.00
$115.22
$118.53
$121.94
$125.44
$129.04
$132.75
$136.57
$140.49
$144.53
$148.68
$152.96
$157.35
$161.87
$166.53
$171.31
$176.23
$181.30
$186.51
$191.87
$197.38
$203.05
$208.89
$214.89
$221.07
$227.42
$233.96
$240.68
$247.60
$254.71
$262.03
$269.56
$277.31
$285.28
$293.48
$301.91
$310.58
$2.86
$5.97
$9.35
$13.00
$16.95
$21.22
$25.84
$30.81
$36.17
$41.94
$48.15
$54.82
$61.99
$69.68
$77.94
$86.79
$96.27
$106.43
$117.31
$128.94
$141.39
$154.69
$168.90
$184.09
$200.30
$217.61
$236.07
$255.77
$276.77
$299.16
$323.03
$348.45
$375.53
$404.37
$435.07
$467.75
$502.53
$539.53
$578.88
$620.74
$0.72
$1.49
$2.34
$3.25
$4.24
$5.31
$6.46
$7.70
$9.04
$10.48
$12.04
$13.70
$15.50
$17.42
$19.48
$21.70
$24.07
$26.61
$29.33
$32.24
$35.35
$38.67
$42.23
$46.02
$50.08
$54.40
$59.02
$63.94
$69.19
$74.79
$80.76
$87.11
$93.88
$101.09
$108.77
$116.94
$125.63
$134.88
$144.72
$155.18
$5.74
$6.07
$6.41
$6.78
$7.17
$7.58
$8.02
$8.48
$8.96
$9.48
$10.02
$10.60
$11.21
$11.85
$12.53
$13.25
$14.01
$14.81
$15.66
$16.56
$17.51
$18.51
$19.57
$20.70
$21.89
$23.14
$24.47
$25.87
$27.36
$28.93
$30.59
$32.34
$34.20
$36.16
$38.23
$40.43
$42.74
$45.20
$47.79
$50.53
$5.02
$5.29
$5.57
$5.87
$6.18
$6.51
$6.86
$7.23
$7.62
$8.04
$8.47
$8.93
$9.41
$9.92
$10.46
$11.03
$11.64
$12.27
$12.94
$13.65
$14.40
$15.19
$16.02
$16.90
$17.83
$18.81
$19.85
$20.95
$22.11
$23.33
$24.62
$25.98
$27.43
$28.95
$30.56
$32.26
$34.05
$35.95
$37.95
$40.07
H
EOQ
Investor's
NAV
$100.00
$105.02
$110.31
$115.88
$121.75
$127.93
$134.45
$141.31
$148.55
$156.17
$164.21
$172.68
$181.61
$191.02
$200.95
$211.41
$222.44
$234.08
$246.35
$259.29
$272.94
$287.34
$302.52
$318.55
$335.45
$353.28
$372.09
$391.95
$412.89
$435.00
$458.33
$482.95
$508.93
$536.36
$565.31
$595.86
$628.12
$662.17
$698.12
$736.07
$776.14
COLUMN
I
Current
Before Fee
MD ROR
5.74%
5.78%
5.81%
5.85%
5.89%
5.93%
5.96%
6.00%
6.03%
6.07%
6.10%
6.14%
6.17%
6.20%
6.23%
6.27%
6.30%
6.33%
6.36%
6.39%
6.41%
6.44%
6.47%
6.50%
6.52%
6.55%
6.58%
6.60%
6.63%
6.65%
6.67%
6.70%
6.72%
6.74%
6.76%
6.78%
6.81%
6.83%
6.85%
6.87%
25%
Proposed
After
After
Fee TWR
Fee TWR Overstatement
20.37%
2.37%
After
Fee IRR
20.30%
J
Current
After Fee
MD ROR
K
Proposed
Before Fee
MD ROR
L
Proposed
After Fee
MD ROR
5.02%
5.04%
5.05%
5.06%
5.08%
5.09%
5.11%
5.12%
5.13%
5.15%
5.16%
5.17%
5.18%
5.20%
5.21%
5.22%
5.23%
5.24%
5.25%
5.26%
5.27%
5.29%
5.30%
5.31%
5.32%
5.33%
5.34%
5.34%
5.35%
5.36%
5.37%
5.38%
5.39%
5.40%
5.41%
5.41%
5.42%
5.43%
5.44%
5.44%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.74%
5.02%
5.00%
4.98%
4.96%
4.95%
4.93%
4.91%
4.90%
4.88%
4.86%
4.85%
4.83%
4.82%
4.81%
4.79%
4.78%
4.77%
4.75%
4.74%
4.73%
4.72%
4.71%
4.70%
4.68%
4.67%
4.66%
4.65%
4.65%
4.64%
4.63%
4.62%
4.61%
4.60%
4.59%
4.59%
4.58%
4.57%
4.56%
4.56%
4.55%
Current
Approach
5.25%
M
Current
Before Fee
TWR Index
$1.00
$1.06
$1.12
$1.18
$1.25
$1.33
$1.41
$1.49
$1.58
$1.67
$1.78
$1.88
$2.00
$2.12
$2.25
$2.39
$2.54
$2.70
$2.88
$3.06
$3.25
$3.46
$3.69
$3.92
$4.18
$4.45
$4.74
$5.06
$5.39
$5.75
$6.13
$6.54
$6.98
$7.44
$7.95
$8.48
$9.06
$9.68
$10.34
$11.04
$11.80
N
Current
After Fee
TWR Index
$1.00
$1.05
$1.10
$1.16
$1.22
$1.28
$1.34
$1.41
$1.49
$1.56
$1.64
$1.73
$1.82
$1.91
$2.01
$2.11
$2.22
$2.34
$2.46
$2.59
$2.73
$2.87
$3.03
$3.19
$3.35
$3.53
$3.72
$3.92
$4.13
$4.35
$4.58
$4.83
$5.09
$5.36
$5.65
$5.96
$6.28
$6.62
$6.98
$7.36
$7.76
Proposed
Approach
4.63%
O
Proposed
Before Fee
TWR Index
$1.00
$1.06
$1.12
$1.18
$1.25
$1.32
$1.40
$1.48
$1.56
$1.65
$1.75
$1.85
$1.95
$2.07
$2.18
$2.31
$2.44
$2.58
$2.73
$2.89
$3.05
$3.23
$3.41
$3.61
$3.81
$4.03
$4.26
$4.51
$4.77
$5.04
$5.33
$5.64
$5.96
$6.30
$6.66
$7.05
$7.45
$7.88
$8.33
$8.81
$9.31
P
Proposed
After Fee
TWR Index
$1.00
$1.05
$1.10
$1.16
$1.22
$1.28
$1.34
$1.40
$1.47
$1.54
$1.62
$1.70
$1.78
$1.87
$1.96
$2.05
$2.15
$2.25
$2.36
$2.47
$2.59
$2.71
$2.83
$2.97
$3.11
$3.25
$3.40
$3.56
$3.73
$3.90
$4.08
$4.27
$4.47
$4.67
$4.89
$5.11
$5.34
$5.59
$5.84
$6.11
$6.39
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
- --
Denominator Issue #2 – Before Fee Denominators Are Frequently Overstated, Causing Understated Before Fee TWRs
1. NCREIF/PREA Standards state:
a. “Before and after fee fund level TWR denominators are the same because there is only one weighted
average equity for the period. The contributions and distributions used in the denominators are always
after fee and are not adjusted to be before fee even when calculating a before fee return.”
2. Before Fee Analysis is Counterfactual and Can Only Be Hypothesized
a. Any reasonable hypothesis implies that the average capital employed will be different
i. For example, a contribution was made to pay the fee, or a distribution was reduced to pay the fee.
b. Modified Dietz (“MD”) denominators assume quarterly period is too long to ignore weighted cash flows,
which include fee cash flows when fees are paid during a quarter.
3. Most logical Way to Deal With This Is To Assume That There Is A Distribution to The Investor Equal To The
Amount Of The Fee Payment – See Spaulding 2011 - “Practical Issues When Calculating Gross and
Net-of-Fees Return”.
a. Otherwise, we would have to speculate as to what rate of return that fee amount would have earned if
left in the portfolio, which is problematic to ascertain, given that the fee payment was not made at BOQ.
b. This means the before fee denominators are too large, causing an understatement of quarterly RORs
i. Except when quarterly before fee RORs are negative
5
This document was presented during the 2016 NCREIF Winter Conference.
The author(s) take full responsibility for all content. This posting is for informational purposes only; neither NCREIF nor its Board express any opinion of the content presented herein.
- --
Denominator Issue #2 (continued)
4. So Impact Is On Before Fee TWRs Only
5. Impacts Any Fee Paying Managed Portfolio, Such as ODCE Funds.
6. Although There Are Many Fee Payments, The Impact Is Expected To Be Minor (Except Perhaps When There Is A
Big Incentive Fee Payment) Estimated At Less Than 0.1% On Average; Perhaps 0.3% In Extreme Scenarios.
7. Although The Error Is Small, Do We Fix This If We Are Already Fixing Issue #1?
6