CHAPTER 2: AI PERFORMANCE & RETURNS Flashcards
WHY IS IT DIFFICULT TO CONDUCT PERFORMANCE APPRAISAL ON AI
- ASYMMETRIC RISK-RETURN PROFILES
- LIMITED PORTFOLIO TRANSPARENCY
- ILLIQUIDITY
- PRODUCT COMPLEXITY
- COMPLEX FEE STRUCTURES
SHARPE RATIO
(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
RISK-ADJUSTED RETURN RATIOS
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
SORTINO RATIO
(Rpf-Rf)/Downside Deviation or Sigma of PF
PROS: Doesn’t penalize upside volatility & instead focus is on downside
CONS: Difficult to calculate
MAR RATIO
Avg CAGR/Max. Drawdown (Since Inception)
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
CALMAR RATIO
Avg CAGR/Max Drawdown (Last 3 years)
Variation of MAR ratio
Fund Avg. CAGR (last 3 years)/Max drawdown (last 3 years)
PRO: Focuses on recent performance
CON: Hides past issues
PE & RE PERFORMANCE EVALUATION
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:
- IRR for PE
- MOIC for PE
- Cap Rate for RE
IRR
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)
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
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
PERFORMANCE OF REAL ESTATE
Cap Rate= Rent/Investment
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)
HEDGE FUNDS: LEVERAGE, ILLIQUIDITY & REDEMPTION TERMS
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
HF: ILLIQUIDITY & REDEMPTION TERMS
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
GAAP ACCOUNTING RULES CATEGORIZE HFs into 3 buckets
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
LEVEL 3
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
TO DISCOURAGE REDEMPTIONS, HFs:
LOCKUP PERIOD
NOTICE PERIOD
REDEMPTION FEES
- Charge redemption fees (typically payable to the remaining investors) to offset the transaction costs for remaining investors
- 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
- 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
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
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
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%?
Vc= 100
Vb= 50
RL= -0.02+(50/100)(-0.02-0.04)= -5%
-2% + 50/100 - (2%-4%)= -6*50/100= -5%
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?
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%
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%
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
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)
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.
HEDGE FUND STRUCTURE
“2 AND 20”
OR
“1 AND 10”
2% MANAGEMENT FEE
20% PERFORMANCE or INCENTIVE FEE or CARRIED INTEREST
AIF ARRANGEMENTS
- Fees based on liquidity terms & asset size
- Founder’s Share
- Either/Or Fees
Fees based on liquidity terms & asset size
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
Founder’s Share
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
Either/Or Fees
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
FUND LIFE STAGES
- Capital Commitment
- Capital Deployment
- Capital Distribution
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)
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.
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%.
- What is the total fee if management fee and incentive fee are calculated independently? What
is the investor’s effective return? - What is the total fee if the incentive fee is calculated after deducting the management fee? Investor’s net return?
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
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%.
- 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?
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
- Calculate the gross return:
Gross return = 30% of $200 million = $60 million
- Calculate the returns in excess of the hurdle rate:
Hurdle rate return = 5% of $200 million = $10 million
- Returns in excess of the hurdle rate = $60 million - $10 million = $50 million
- Calculate the management fee:
Management fee = 2% of $200 million = $4 million
- Calculate the performance fee:
Performance fee = 20% of $50 million = $10 million
- 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%
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%.
- 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?
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
- Calculate the management fee:
Management fee = 2% of $220 million = $4.4 million - 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. - 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.
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%.
- In the third year, the fund value increases to 256 million. What is the total fee and investor’s net return?
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%
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.
- Calculate the return to the investor of investing directly in HF.
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%
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.
- 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.
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%
Relative Alternative Investment Returns and
Survivorship Bias
Hedge Fund Index Returns Overstatement: SURVIVORSHIP BIAS & BACKFILL BIAS
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
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.
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
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
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.
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%
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%
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
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.
