CHAPTER 2: AI PERFORMANCE & RETURNS

Question 1

WHY IS IT DIFFICULT TO CONDUCT PERFORMANCE APPRAISAL ON AI

Answer 1

1. ASYMMETRIC RISK-RETURN PROFILES
2. LIMITED PORTFOLIO TRANSPARENCY
3. ILLIQUIDITY
4. PRODUCT COMPLEXITY
5. COMPLEX FEE STRUCTURES

Question 2

SHARPE RATIO

Answer 2

(Rpf-Rf)/Sigma or SD of portfolio
SD measures volatility

PROS: Easy to calculate

CONS:
- Penalizes both upside & downside volatility equally (only left side curve volatility is dangerous in the sigma normal distribution curve i.e. symmetrical distribution on both LHS & RHS)
- Assumes normal distribution.

However, AIs often display non-normal return distributions with signficiant skewness & kurtosis. This makes sharpe ratio a less-than-ideal performance measure for AIs

Question 2

RISK-ADJUSTED RETURN RATIOS

Answer 2

STSC: sigma, beta, downside sigma, max drawdown

SHARPE: (Rpf-Rf)/sigma pf
TREYNOR: (Rpf-Rf)/B
SORTINO: (Rpf-Rf)/downside sigma
SD doesn’t differentiate upside or downside risk; in long-term investing- upside risk isn’t really a risk
CALMAR: (Rpf-Rf)/max drawdown

Jensen’s Alpha: Rpf-Ke

Question 2

SORTINO RATIO

Answer 2

(Rpf-Rf)/Downside Deviation or Sigma of PF

PROS: Doesn’t penalize upside volatility & instead focus is on downside

CONS: Difficult to calculate

Question 3

MAR RATIO

Avg CAGR/Max. Drawdown (Since Inception)

Answer 3

Measures average return relative to the worst drawdown loss (distance between a peak & trough of a portfolio). It uses full-investment history of portfolio since inception

MAR RATIO= Fund Avg. CAGR (since inception)/Max Drawdown (since inception)

Higher the MAR ratio, better an AI asset performed on a risk-adjusted basis over a specific period of time

PRO: Shows entire history
CON: doesn’t specifically focus on recent performance which may be more relevant for the investor

Question 4

CALMAR RATIO

Avg CAGR/Max Drawdown (Last 3 years)

Answer 4

Variation of MAR ratio

Fund Avg. CAGR (last 3 years)/Max drawdown (last 3 years)

PRO: Focuses on recent performance
CON: Hides past issues

Question 5

PE & RE PERFORMANCE EVALUATION

Answer 5

BOTH have a J-CURVE EFFECT
Initial -ve decline followed by strong growth over long-term

Both require significant initial cash outlays & investments take some time to turn profitable

Thus, short-term performance measures must NOT be used. Instead use:

1. IRR for PE
2. MOIC for PE
3. Cap Rate for RE

Question 5

IRR

Answer 5

ASSUME NPV= 0 (Breakeven Point)
IRR= discount rate that makes NPV= 0

0 = -Inv + CF/(1+r)^n + CF/(1+r)^n+1…
IRR= make CFs equal to inital investment
Inv= CF/(1+R)^N + CF/(1+R)^N+2
If R>r, then accept; else reject
i.e. IRR>WACC= accept; else reject

R= opportunity cost of capital or minimum rate of return

ASSUMPTIONS:
- must know about cost of financing outgoing CFs (typically WACC) & Reinvestment Rate assumptions (i.e. reinvested @IRR rate) for outgoing CFs to make incoming CFs (must be assumed & may not be earned)

Question 6

PERFORMANCE OF PRIVATE EQUITY

MULTIPLE OF INVESTED CAPITAL (MOIC)

eg: (Realized+Unrealized)/Total Inv Capital

eg: 1.2
means
1= starting point
20%= what you’ve earned on top

Answer 6

To overcome complexity/drawbacks of IRR, MOIC or money multiple is used

Simply measures the total value of all distributions
and
residual asset values relative to an initial total investment

MOIC= (Realized Value of Inv + Unrealized Value of Inv) / Total amount of Invested Capital

Although simple to calculate, a major drawback of MOIC is that it ignores the TIMING of CFs

Question 7

PERFORMANCE OF REAL ESTATE

Cap Rate= Rent/Investment

Answer 7

Cap rate= Rent/Investment

Cap rate is r-g in Gordon’s growth model

Value of Property= Rent/Cap Rate

Calculated as annual rent actually being earned divided by the price originally paid for the property

eg: 10M/100M= 10%
10% is cap rate

CAP RATE= CAPITALIZATION RATE

Used to value properties
eg:
Giving $10M Rent/0.1 i.e. cap rate of similar properties to come up w property’s value (based on relative valuation)

Question 8

HEDGE FUNDS: LEVERAGE, ILLIQUIDITY & REDEMPTION TERMS

Answer 8

LEVERAGE: used to enhance returns

To lever their portfolio, HFs use derivatives or borrow capital from prime brokers

HFs must deposit cash or other collateral into a margin account w the prime broker, who then lends securities to the HF

If the margin account falls below a certain threshold, a margin call is issued, and the HF is required to put up additional collateral

This can magnify a HF’s losses because it may have to liquidate the losing position to meet the margin call

eg: deposited 100M w broker as margin
LONG 1000M
SHORT 1000M
Beta= 0
Both positions offset each other
Now,
LONG 1000M: 10% gain
SHORT 1000M: 8% loss
2% net profits

2% * 1000M= 20M profits
20M made over 100M deposits = 20/100= 20%
Leverage used to multiply returns

Question 9

HF: ILLIQUIDITY & REDEMPTION TERMS

Answer 9

HFs are valued on a daily, weekly, monthly &/or quarterly basis

Value of HF depends on Value of underlying positions

Price used for valuation depends on whether market prices are available & if the underlying position is liquid

When market prices are available, the fund decides what price to use

Common practice is to quote at the average of the bid & ask prices

A conservative approach is to use bid prices for long & ask prices for short

Question 10

GAAP ACCOUNTING RULES CATEGORIZE HFs into 3 buckets

Answer 10

L1= use publicly traded prices
L2= use broker quotes
3= use internal models

LEVEL 1: Exchange-traded; publicly traded price is available & is used for valuation purposes

LEVEL 2: when such price isn’t available, outside broker quotes are used.

LEVEL 3: when broker quotes aren’t available or are unreliable, as a final recourse, assets are valued using internal models

Question 11

LEVEL 3

Answer 11

L3 asset values require additional scrutiny from investors

Models used must be APPROPRIATE + CONSISTENT

Values obtained may not reflect true liquidation values.

Also, the returns may be smoothed & volatility understated

Another factor that can magnify losses for HFs is REDEMPTION PRESSURE

Redemptions usually occur when HF is performing poorly

Redemptions can force HF managers to liquidate positions at disadvantageous prices

Question 12

TO DISCOURAGE REDEMPTIONS, HFs:

LOCKUP PERIOD
NOTICE PERIOD
REDEMPTION FEES

Answer 12

1. Charge redemption fees (typically payable to the remaining investors) to offset the transaction costs for remaining investors
2. Use notice periods (investors need to inform the fund manager in advance before making redemption) which provides the HF manager an opportunity to liquidate positions in an orderly manner
3. HFs use lockup period (time periods when investors can’t withdraw their capital) which provides the HF manager sufficient time to implement his inv strategy

Question 13

A PE closes a fund w a capital commitment of 750M euros. It has a capital call of 500M euros initially & another 250M euros at end of Y1. The management fee is 2% per annum. At the end of Y5, a total of 1B euros is distributed to its investors, and the fund is left w 500M euros in asset value. Calculate fund’s MOIC

Answer 13

MOIC= Realized Val+Unrealized Val/Total IC

IC= total paid-in capital - management fees & fund expenses

MOIC is diff from IRR because it ignores timing of CFs

Total Paid in capital= 500+250= 750
Total Management fee for 5 years= 7500.025= 75
Total IC= 750-75= 675

MOIC= (1000+500)/675= 2.2x

Question 14

Scenario 2: Suppose the fund’s underlying positions incur a loss of 2% instead of earning a gain. What would have been the leveraged return if the fund had borrowed $50M at 4%?

Answer 14

Vc= 100
Vb= 50
RL= -0.02+(50/100)(-0.02-0.04)= -5%

-2% + 50/100 - (2%-4%)= -6*50/100= -5%

Question 14

A HF w $100M Capital normally uses leverage to invest in a variety of equity-linked notes

Scenario 1: Suppose the fund’s underlying positions return 8%. If it could add leverage of $50M to the portfolio at a funding cost of 4% what would have been the leveraged return?

Answer 14

Leveraged Return:

Vc=100
Vb= 50
RL= 0.08 + (50/100) (0.08-0.04)= 10%

Leverage= 50/100
Return= 8%100/100 + (8-4%)50/100= 10%

Question 15

Atrium Opportunity Fund LLC hedge fund has USD150 million of capital. It generally uses leverage to invest in equity-linked notes. Suppose Atrium’s underlying positions return 9%. If it could add leverage of USD50 million to the portfolio at a funding cost of 5%, its leveraged return would have been closest to:

A. 10.33%
B. 7.7%
C. 11.2%

Answer 15

Initial= 150M
Leverage= 50M
Total= 150+50= 200M

Unleveraged Return:
150*0.09= 13.5

Leveraged Return:
50(0.09-0.05)= 0.0450= 2

Total Return= 13.5+2= 15.5

Leveraged Return %= Total Return/Original Capital
= 15.5/150= 10.33

Question 16

A private equity firm makes an initial investment of USD4.7 billion into ABC company in Year 0. Seven years later, it sells its stake in the company for USD9.3 billion. Additional capital investments were made in Year 2 and in Year 3 for USD1.3 billion and USD500 million, respectively. Its MOIC is closest to:

A. 1.43x
B. 6%
C. Neither A) nor B)

Answer 16

Initial= 4.7B
New Inv= 1.3B
New Inv= 0.5B
Sell (after 7 years)= 9.3B

MOIC= (Realized+Unrealized)/Total IC

9.3/(4.7+1.3+0.5)= 9.3/6.5= 1.430
1.43x

i.e.
Started at 1 & increased to 43%
A.

Question 17

HEDGE FUND STRUCTURE

“2 AND 20”
OR
“1 AND 10”

Answer 17

2% MANAGEMENT FEE
20% PERFORMANCE or INCENTIVE FEE or CARRIED INTEREST

Question 18

AIF ARRANGEMENTS

Answer 18

1. Fees based on liquidity terms & asset size
2. Founder’s Share
3. Either/Or Fees

Question 19

Fees based on liquidity terms & asset size

Answer 19

HFs may provide a fee discount to investors who are willing to accept lower liquidity eg: longer lockups

Similarly, HFs may provide a fee discount

These terms are negotiated w individual investors via side letters, which are special amendments to the fund’s LPA

Question 20

Founder’s Share

Answer 20

To entice early participation in new HFs, managers often offer incentives called founder’s class shares

These shares have a lower fee structure eg: “1.5 and 10” instead of “2 and 20” and are typically applicable to a certain cutoff threshold eg: first 100M in assets

Question 21

Either/Or Fees

Answer 21

A few large institutional investors have started working w this new fee model

EITHER charge a 1% management fee or to receive a 30% incentive fee above a mutually agreed-on hurdle rate, whichever is greater

The 1% management fee allows a fund to cover its expenses during down years & the 30% incentive fee incentivizes and rewards managers during up years

Question 22

FUND LIFE STAGES

Answer 22

1. Capital Commitment
2. Capital Deployment
3. Capital Distribution

Question 23

A PE fund invests $10 million in Portfolio company A and $12 million in portfolio company B.
Company A generates a $6 million profit, but Company B generates a $7 million loss. The time
period for the gain and loss are the same. The manager’s carried interest incentive fee is 20% of
profits. Calculate the incentive fee under:
1. A European-style waterfall whole-of funds approach
2. An American-style waterfall deal-by-deal basis (assuming no clawback)

Answer 23

Solution to 1:
Overall, the fund lost money (+$6 million - $7 million = -$1 million) so under a European-style whole-of-fund waterfall, the manager will not receive any incentive fee

Solution to 2:
Under an American-style waterfall, the GP could still earn 20% x $6 million = $1.2 million as incentive fees on the profitable Company A deal.

Question 24

Consider a hedge fund with an initial investment of 200 million; the fee structure is 2 and 20 and is based on year-end valuation. In year 1, the return is 30%.

1. What is the total fee if management fee and incentive fee are calculated independently? What
   is the investor’s effective return?
2. What is the total fee if the incentive fee is calculated after deducting the management fee? Investor’s net return?

Answer 24

30% * 200= 60
So, 200 goes up to 260

2001.3= 260
Profit= 60
Management Fee= 0.02260= 5.2M
Incentive Fee= 20%*60= 12M
Total Fee= 12+5.2= 17.2 M
Profit Without Fees= 260-17.2/200 -1= 21.4%

Incentive fee is calculated after deducting management fee?

Incentive fee after deducting management fee= 20% * (260-200-5.2)= 10.96

Total Fee= 5.2+10.96= 16.16M

Investor’s Return= 260-16.16/200 - 1 = 21.92%
As you can see, the return is better than Part 1 because incentive fee paid is relatively less here

Question 25

Consider a hedge fund with an initial investment of 200 million; the fee structure is 2 and 20 and is based on year-end valuation. In year 1, the return is 30%.

3. If there is a hurdle rate of 5% and fees are based on returns of in excess of 5%, what is the total fee? What is the investor’s net return?

Answer 25

Initial investment: $200 million
Fee structure: 2 and 20
2% management fee on the total assets under management
20% performance fee on returns in excess of the hurdle rate
Hurdle rate: 5%
Year 1 return: 30%

Calculating the Total Fees

1. Calculate the gross return:

Gross return = 30% of $200 million = $60 million

2. Calculate the returns in excess of the hurdle rate:

Hurdle rate return = 5% of $200 million = $10 million

3. Returns in excess of the hurdle rate = $60 million - $10 million = $50 million
4. Calculate the management fee:

Management fee = 2% of $200 million = $4 million

5. Calculate the performance fee:

Performance fee = 20% of $50 million = $10 million

6. Total fees = Management fee + Performance fee
   Total fees = $4 million + $10 million = $14 million

Investor’s net return = Gross return - Total fees

Investor’s net return = $60 million - $14 million = $46 million

Investor’s Return= $46 million / $200 million × 100 = 22.92%

Question 26

Consider a hedge fund with an initial investment of 200 million; the fee structure is 2 and 20 and is based on year-end valuation. In year 1, the return is 30%.

4. In the second year, the fund declines to 220 million. Assume that management fee and incentive fee are calculated independently as indicated in Part 1, but now a high-water mark is also used in fee calculations. What is the total fee? What is the investor’s net return?

Answer 26

Initial investment: $200 million
Fee structure: 2 and 20
2% management fee on the total assets under management
20% performance fee on returns in excess of the hurdle rate
Year 1 return: 30%

Hard vs Soft Hurdle. In this case, it’s a HARD hurdle.

High-water mark: $260 million (from the 30% return in year 1)
Year 2 valuation: $220 million

Calculating the Total Fees

1. Calculate the management fee:
   Management fee = 2% of $220 million = $4.4 million
2. Calculate the performance fee:
   Since the fund value of $220 million is below the high-water mark of $260 million, no performance fee is charged.
3. Total fees = Management fee + Performance fee
   Total fees = $4.4 million + $0 million = $4.4 million

Investor’s net return = $220 million - $4.4 million = $215.6 million

The investor’s net return is $215.6 million, which is -11.2% of the initial investment of $200 million.

Question 27

Consider a hedge fund with an initial investment of 200 million; the fee structure is 2 and 20 and is based on year-end valuation. In year 1, the return is 30%.

5. In the third year, the fund value increases to 256 million. What is the total fee and investor’s net return?

Answer 27

Initial investment: 200 million
Fee structure: 2% management fee, 20% incentive fee
Year 1 return: 30%
Fund value in third year: 256 million

Calculation Steps:

Management fee:

Fund value = 256 million
Management fee = 256 x 0.02 = 5.12 million
Incentive fee:

High water mark = 242.8 million
Fund value exceeds high water mark
Incentive fee = (256 - 242.8) x 0.2 = 2.64 million
Total fee:

Management fee + Incentive fee = 5.12 + 2.64 = 7.76 million
Investor’s net return:

Net value = 256 - 7.76 = 248.24 million
Initial investment = 215.6 million (after previous year’s growth and fees)
Investor’s net return = (248.24 / 215.6) - 1 = 15.14%

Question 28

An investor is contemplating investing £200 million in either the Hedge Fund (HF) or the Fund of Funds (FOF). FOF has a “1 and 10” fee structure and invests 10% of its assets under management
in HF. HF has a standard “2 and 20” fee structure with no hurdle rate. Management fees are
calculated on an annual basis on assets under management at the beginning of the year.

Management fees and incentive fees are calculated independently. HF has a 25% return for the year before management and incentive fees.

1. Calculate the return to the investor of investing directly in HF.

Answer 28

Investing in Hedge Fund (HF)

Investment= 200M
2:20= Management:Incentive
25% Return

Profit before fees: £200 million × 25% = £50 million
Management fee: £200 million × 2% = £4 million
Incentive fee: £50 million × 20% = £10 million
Net profit: £50 million - £4 million - £10 million = £36 million
Return to investor: £36 million / £200 million = 18%

Question 29

An investor is contemplating investing £200 million in either the Hedge Fund (HF) or the Fund of Funds (FOF). FOF has a “1 and 10” fee structure and invests 10% of its assets under management
in HF. HF has a standard “2 and 20” fee structure with no hurdle rate. Management fees are
calculated on an annual basis on assets under management at the beginning of the year.
Management fees and incentive fees are calculated independently. HF has a 25% return for the year before management and incentive fees.

2. Calculate the return to the investor of investing in FOF. Assume that the other investments in
   the FOF portfolio generate the same return before management fees as HF and have the same fee structure as HF.

Answer 29

FOF: A pooled investment fund that invests in other hedge funds.

Structure: FOF charges its own management and incentive fees, on top of fees charged by underlying hedge funds.

Investing in Fund of Funds (FOF)

Investment= 200M
1:10= Management:Incentive= On AUM:On Profit after HF Fees
25% Return

Profit after HF fees: £200 million × 18% = £36 million
FOF management fee: £200 million × 1% = £2 million
FOF incentive fee: £36 million × 10% = £3.6 million
Net profit: £36 million - £2 million - £3.6 million = £30.4 million
Return to investor: £30.4 million / £200 million = 15.2%

Question 30

Relative Alternative Investment Returns and
Survivorship Bias

Hedge Fund Index Returns Overstatement: SURVIVORSHIP BIAS & BACKFILL BIAS

Answer 30

Survivorship Bias

Poor performers excluded; skews returns upwards
Index includes only surviving funds over time
Overstates index returns by excluding failed funds

Backfill Bias
HFs only report returns after a successful period; skews returns upwards

New fund’s historical returns added when it enters the database
Overstates index returns as well-performing funds are more likely added

Question 31

Clawbacks Due to Return Timing Differences

A PE fund makes two investments for $5 million each in Company A and Company B. One year later Company A returns a $8 million profit. But two years later Company B turns out to be a complete bust and is worth zero.

The GP’s carried interest is 20% of aggregate profits and there is a clawback provision. How much carried interest will the GP receive in year 1 and year 2.

Answer 31

Initial Investments:
$5 million each in Company A and Company B

Year 1:
Company A Profit: $8 million
GP Carried Interest: 20% of $8 million = $1.6 million (held in escrow, not paid)

Year 2:

Company B Loss: Worth zero
Net Aggregate Profit: $8 million (Company A) - $5 million (Company B) = $3 million
GP Carried Interest: 20% of $3 million = $0.6 million
Clawback: GP returns $1 million ($1.6 million - $0.6 million) to LPs due to clawback provision

Question 32

A PE fund invests USD15 million in Portfolio Company A and USD17 million in Portfolio Company B. Company A generates a USD5 million profit, but Company B generates a USD6 million loss. The time period for the gain and loss are the same. The manager’s carried interest incentive fee is 20% of profits. The incentive fee under a European-style waterfall whole-of funds approach is:

A. 0
B. USD 1M
C. USD 0.2M

Answer 32

CoA= 15M: generates 5M profit
CoB= 17M: generates 6M loss
Total= 32M

Net=
CoA: 15+5= 20
CoB: 17-6= 11
Total= 31M

1M Loss

Under the European-style waterfall, the carried interest incentive fee is calculated on the total profits of the entire fund.

Since the net result is a loss (-$1 million), there are no profits to calculate the incentive fee on.
Incentive Fee:

As there are no net profits, the incentive fee is $0.

Answer: A.

Question 33

An investor is contemplating investing €100 million in either the RS Hedge Fund (RS HF) or the UV Fund of Funds (UV FOF). UV FOF has a “1 and 10” fee structure and invests 10% of its AUM in RS HF. RS HF has a standard “2 and 20” fee structure with no hurdle rate. Management fees are calculated on an annual basis on AUM at the beginning of the year. Assume that management fees and incentive fees are calculated independently. RS HF has a 30% return for the year before management and incentive fees.

Assume that the other investments in the UV FOF portfolio generate the same return before management fees as those of RS HF. The return to the investor from investing in UV FOF is closest to:

A. 22.0%
B. 18.8%
C. 18.46%

Answer 33

100M

RS HF: 2:20= Management:Incentive
No Hurdle Rate
30% return

UV FOF: 1:10= Management:Incentive
10% AUM invested in HF

A. FOR RS HF:

Initial Investment: €100 million
Return Before Fees: 30%
Profit before fees: €100 million × 30% = €30 million
Management Fee: 2% of €100 million = €2 million
Incentive Fee: 20% of €30 million = €6 million
Net Profit: €30 million - €2 million - €6 million = €22 million
Net Return to Investor: €22 million / €100 million = 22%

B. FOR UV FOF:

I). RS HF Portion:
Investment in RS HF: 10% of €100 M = €10 million
Return Before Fees: 30%

Profit before fees: €10 million × 30% = €3 million
Management Fee: 2% of €10 million = €0.2 million
Incentive Fee: 20% of €3 million = €0.6 million
Net Profit: €3 million - €0.2 million - €0.6 million = €2.2 million

II). Other Investments Allocation:

Inv. in other investments: 90% of €100M = €90M
Return Before Fees: 30%

Profit before fees: €90 million × 30% = €27 million
Management Fee: 2% of €90 million = €1.8 million
Incentive Fee: 20% of €27 million = €5.4 million
Net Profit: €27 million - €1.8 million - €5.4 million = €19.8 million

FOF Total Net Profit: €2.2 million (RS HF) + €19.8 million (Other investments) = €22 million

Now,
UV FOF Fees:

Management Fee: 1% of €100 million = €1 million
Incentive Fee: 10% of €22 million = €2.2 million

Net Profit for UV FOF:

Net Profit: €22M - €1M - €2.2M = €18.8 million
Net Return to Investor: €18.8M/ €100M = 18.8%

Question 34

A PE fund makes two investments for USD10 million each in Company A and Company B. One year later Company A returns a USD13 million profit. But two years later Company B turns out to be a complete bust and is worth zero. The GP’s carried interest is 20% of aggregate profits and there is a clawback provision. How much carried interest will the GP receive in year 2?

A. $2.6M
B. $0.6M
C. $0

Answer 34

Y1= CoA= 10M: returns 13M Profit
Y2= CoB= 10M: goes to 0: 10M Loss

20M became 23M total
3M net
So, 20%*3M= 0.6

OR

Second Method:
Clawback Provision

20% aggregate profits

Y1: 20%13M= 2.6M (goes to escrow for benefit of GP & not actually paid)
20%0M= 0

In Y2, GP loses 10M of initial 13M gain. So, aggregate profit is 3M.

The clawback provision requires the GP to return previously received carried interest if subsequent losses reduce the overall profit.

The carried interest payable is 20%*3M= $ 0.6M

The GP has to return 2M USD of previously accrued incentive fee to the LPs because of this clawback position

So, return 0.6M

B.