IFT Notes for Level I CFA^{®} Program

This learning module covers:

- Issues in performance appraisal of alternative investments
- Calculating fees and returns of alternative investments

It can be difficult to conduct performance appraisal on alternative investments because these investments have the following characteristics:

- asymmetric risk–return profiles
- limited portfolio transparency
- illiquidity
- product complexity
- complex fee structures

The commonly used ratios in the performance appraisal of alternative investments include:

- Sharpe ratio
- Sortino ratio
- MAR ratio
- Calmar ratio

**Sharpe ratio**

The Sharpe ratio measures return per unit of risk. It is calculated as:

Sharpe ratio=

__Pros__:

- It is easy to calculate.

__Cons__:

- It penalizes both upside and downside volatility equally.
- It assumes a normal distribution. However, alternative investments often display non-normal return distributions with significant skewness and kurtosis. This makes the Sharpe ratio a less-than-ideal performance measure for alternative investments.

**Sortino ratio**

The Sortino ratio measures return relative to downside volatility. It is calculated as:

Sortino ratio=

__Pros__:

- It does not penalize upside volatility and is instead focused on downside deviation.

__Cons__:

- It is more difficult to calculate.

**MAR ratio**

The MAR ratio measures average return relative to the worst drawdown loss (distance between a peak and a trough of a portfolio). It uses the full investment history of the portfolio since inception.

It is calculated as:

MAR ratio=

The higher the MAR ratio, the better an alternative asset performed on a risk-adjusted basis over a specific period of time.

__Pros__:

- It shows the entire history.

__Cons__:

- It does not specifically focus on recent performance which may be more relevant for the investor.

**Calmar ratio**

The Calmar ratio is a variation of the MAR ratio and it uses the last three years of performance data instead of the full investment history.

It is calculated as:

Calmar ratio=

__Pros__:

- It focuses on the recent performance

__Cons__:

- It might hide past issues

Private equity and real estate investments often display a **J-curve effect** – initial decline followed by strong growth over the long term. This is because both private equity and real estate require significant initial cash outlays, and the investments take some time to turn profitable. Therefore, it is inappropriate to use short-term performance measures for private equity and real estate. Instead, the following measures are commonly used.

__Performance measures for private equity__:

The **IRR calculation** is frequently used to evaluate private equity investments. However, the determination of an IRR involves certain assumptions about a financing rate to use for outgoing cash flows (typically a weighted average cost of capital) and a reinvestment rate assumption to make on incoming cash flows (which must be assumed and may or may not actually be earned).

To overcome this complexity, the **multiple of invested capital (MOIC),** or money multiple is frequently used. It simply measures the total value of all distributions and residual asset values relative to an initial total investment.

MOIC = (Realized value of investment + Unrealized value of investment)/(Total amount of invested capital).

Although simple to calculate, a major drawback of MOIC is that it ignores the timing of the cash flows.

__Performance measures for real estate__:

The **cap rate** is often used to evaluate real estate investments. It is calculated as the annual rent actually being earned divided by the price originally paid for the property.

**Leverage**

Hedge funds often use leverage to enhance returns. To lever their portfolio hedge funds use derivatives or borrow capital from prime brokers. Hedge funds must deposit cash or other collateral into a margin account with the prime broker, who then lends securities to the hedge fund. If the margin account falls below a certain threshold, a margin call is issued, and the hedge fund is required to put up additional collateral. This can magnify a hedge fund’s losses because it may have to liquidate the losing position to meet the margin call.

**Illiquidity and Potential Redemption Pressures**

Hedge funds are valued on a daily, weekly, monthly, and/or quarterly basis. The value of a hedge fund depends on the value of underlying positions.

The price used for valuation depends on whether market prices are available and 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 and ask prices. A conservative approach is to use bid prices for long and ask prices for short.

GAAP accounting rules categorize hedge fund investments into three buckets:

__Level 1__: An exchange-traded, publicly traded price is available and is used for valuation purposes.__Level 2__: When such price is not available, outside broker quotes are used.__Level 3__: When broker quotes are not available or are unreliable, as a final recourse, assets are valued using internal models.

Level 3 assets values require additional scrutiny from investors. The models used should be appropriate and consistent. The values obtained may not reflect true liquidation values. Also, the returns may be smoothed and the volatility understated.

Another factor that can magnify losses for hedge funds is redemption pressure. Redemptions usually occur when the hedge fund is performing poorly. Redemptions can force hedge fund managers to liquidate positions at disadvantageous prices.

To discourage redemptions:

- Hedge funds sometimes charge redemption fees (typically payable to the remaining investors) to offset the transaction costs for the remaining investors.
- Hedge funds use notice periods (investors need to inform the fund manager in advance before making a redemption) which provide the hedge fund manager an opportunity to liquidate positions in an orderly manner.
- Hedge funds use lockup period (time periods when investors cannot withdraw their capital) which provide the hedge fund manager sufficient time to implement his investment strategy.

Hedge funds commonly use a “2 and 20” fee structure and fund of funds commonly use the “1 and 10” fee structure. However, many variations of the fee structure exist.

Analysts should be aware of any custom fee arrangements in place that will affect the calculation of fees and performance. These can include such arrangements such as:

**Fees based on liquidity terms and asset size**: Hedge funds may provide a fee discount to investors who are willing to accept lower liquidity e.g., longer lockups. Similarly, hedge funds may provide a fee discount to larger investors. These terms are negotiated with individual investors via side letters, which are special amendments to the fund’s LPA.**Founder’s share**: To entice early participation in new hedge funds, managers often offer incentives known as founder’s class shares. These shares have a lower fee structure e.g., “1.5 and 10” instead of “2 and 20” and are typically applicable to a certain cutoff threshold e.g., the first $100 million in assets.**Either/or fees**: A few large institutional investors have recently worked out a new fee model with some hedge fund managers. These managers agree__either__to 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 and the 30% incentive fee incentivizes and rewards managers during up years.

**Example: Incentive Fees Relative to Waterfall Types**

(*This is based on Example 4 from the curriculum.*)

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:

- A European-style waterfall whole-of funds approach
- 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 manger 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.

**Example: Fee and return calculations**

(*This is based on Example 5 from the curriculum.*)

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

**Solution:**

1. Initial investment grows to: 200 x 1.3 = $260 million.

Profit = $60 million.

Management fee: 0.02 x 260 = $5.2 million.

Incentive fee which is 20% of profit = 20% x 60 = $12 million.

Total fee = $5.2 million + $12 million = $17.2 million.

Investor’s return = (260-17.2)/200-1 = 21.4%

Incentive fee after deducting management fee = 20% x (260 – 200 – 5.2) = 10.96.

Total fee = 5.2 + 10.96 = $16.16 million.

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.

3. There is a hurdle rate of 5%. So, 200 x 0.05 = $10 million must be subtracted before incentive fees are paid.

Incentive fee = 0.2 x (260 – 200 – 5.2 – 10) = 8.96.

Total fee = 5.20 + 8.96 = $14.16 million.

Incentive fee is further reduced and the investor’s return is enhanced.

Investor’s return = (260-14.16)/200-1 = 22.92%.

4. Management fee = 0.02 x 220 = 4.4. To calculate the incentive fee, we need to determine whether the fund value has exceeded the high-water mark. The high-water mark was achieved at the end of Year 1. This value was 260 million – 17.2 million = 242.8 million. The incentive fee is 0 because the fund value is below the high-water mark. Hence the total fee = $4.4 million.

Investor’s return = (220-4.4)/242.8-1 = -11.2%

5. Management fee = 256 x .02 = 5.12. Since $256 has exceeded high water mark of 242.8 million, an incentive fee would be paid. Incentive fee = (256 – 242.8) x 0.2 = 2.64. Total fee = 5.12 + 2.64 = 7.76 million.

Investor’s net return = (256- 7.76)/215.6-1 = 15.14%.

**Example: Hedge fund versus fund of funds**

(*This is based on Example 6 from the curriculum.*)

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.
- 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.

**Solution to 1: **

HF has a profit before fees on a £200 million investment of £50 million (= 200 million × 25%). The management fee is £4 million (= 200 million × 2%) and the incentive fee is £10 million (= 50 million × 20%). The return to investor is 18% (= (50 – 4 – 10) / 200).

**Solution to 2: **

FOF earns an 18% return or £36 million profit after fees on £200 million invested with hedge funds. FOF charges the investor a management fee of £2 million (= 200 million × 1%) and an incentive fee of £3.6 million (= 36 million × 10%). The return to the investor is 15.2% (= (36 – 2 -3.6) / 200).

Hedge fund index returns can be overstated due to survivorship, and backfill biases.

- Survivorship bias occurs when an index is composed of only surviving funds over a period of time, which tends to overstate the index returns.
- Backfill bias occurs when a new fund enters a database and historical returns of that fund are added (i.e., “backfilled”). Usually, funds that performed well are added which tends to overstate the index returns.

**Example: Clawbacks Due to Return Timing Differences**

(This is based on Example 7 from the curriculum.)

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.

**Solution**:

In year 1, the GP will receive a carried interest of 20% of $8 million = $1.6 million. This amount would typically be held in an escrow account for the benefit of the GP but not actually paid.

In year 2, the GP loses $5 million of the initial $8 million gain, so the aggregate profit is only $3 million. The carried interest payable is 20% x $3 million = $0.6 million. The GP has to return $1 million of the previously accrued incentive fee to the LPs because of the clawback provision.