###### Valuating and Calculating Returns on A ...

Hedge Funds Valuating and calculating returns for hedge funds include issues such as... **Read More**

In discussing alternative investment returns, consider hedge funds. Hedge funds employ intricate strategies to generate high returns with low correlation to the broader market. These strategies necessitate the use of sophisticated portfolio management tools and a wide range of skills, making them more costly to operate. Instead of paying a high flat management fee, investors prefer a portion of the compensation to be tied to the performance delivered by the strategy, known as a **performance fee**.

There are also other complex compensation arrangements that aim to align the interests of the manager and the investor. These structures are designed to reward investors for early involvement, larger investments, and/or longer lockup periods. For example, a hedge fund might offer a lower management fee for investors who commit their capital for a longer period. These complex fee structures affect returns for different investors in the same fund, as well as returns before and after fees across various alternative investments.

Investor redemptions can lock in or amplify losses for hedge funds. Redemptions often occur when a hedge fund is underperforming. For instance, if a hedge fund loses 20% of its value, investors might start to redeem their shares, forcing the fund to sell assets to meet these redemptions. This could potentially force the hedge fund manager to liquidate some positions, potentially receiving particularly unfavorable prices due to redemption pressures while also incurring transaction costs.

A hedge fund’s ability to demand a long lockup period while raising a significant amount of investment capital largely depends on the reputation of the firm or the hedge fund manager. For example, a well-known hedge fund manager with a successful track record might be able to demand a 2-year lockup period, while a less-known manager might only be able to demand a 1-year lockup period.

Funds of hedge funds may provide more redemption flexibility than direct investors in hedge funds due to special redemption arrangements with the underlying hedge fund managers, the maintenance of additional cash reserves, access to temporary bridge-loan financing, or simply avoiding less liquid hedge fund strategies. For instance, a fund of hedge funds might have a redemption period of 90 days, while the underlying hedge funds might have a redemption period of 180 days.

Redemption terms should ideally be designed to match the expected liquidity of the assets being invested in. However, even with careful planning, an initial drawdown can escalate into something much more serious when it involves illiquid and obscure assets. These events are not easily modeled. For example, a hedge fund that invests in illiquid assets like private equity might have a redemption period of 1 year, while a hedge fund that invests in liquid assets like stocks might have a redemption period of 30 days.

Alternative investments often involve customized fee arrangements that combine management and performance-based fees. These fees can vary based on the size, timing, and terms of an investor’s participation in the investment over time.

**Fee Arrangement Based on Liquidity Terms and Asset Size:**

For instance, in the real world, Limited Partnerships (LPs) such as Blackstone or KKR may charge different rates depending on the liquidity terms that an investor is willing to accept, with longer lockups resulting in lower fees. Managers may also offer discounts on their fees for larger investors or for placement agents who introduce these investors.

Smaller investment funds that exhibit strong performance and have limited capacity may choose to sustain higher fees. They might even opt to turn away larger investors rather than accepting lower fee arrangements.

**Founders Shares:**

Managers sometimes offer incentives known as founder’s class shares to entice early participation in startup funds. For example, a new hedge fund might offer founders shares that entitle investors to a lower fee structure. These may apply only to the first $100 million in assets invested, although cutoff thresholds vary. An additional option is to decrease fees for early founder’s share investors when the fund reaches specific critical mass or performance milestones.

**“Either/Or” Fees:**

Significant institutional investors have urged alternative investment funds to adopt a mutually exclusive fee structure, requiring them to decide between a fixed management fee or a variable performance fee.

For instance, managers commit to either applying a lower 1% management fee to cover expenses in less favorable years or accepting a higher 30% incentive fee above an annually agreed-upon hurdle to motivate and reward managers in profitable years, whichever is higher.

Return calculations for alternative investments can vary significantly based on the nature of the investments. For instance, more liquid alternative investments such as Real Estate Investment Trusts (REITs), commodity index exchange-traded funds, or other frequently traded investments typically have a straightforward management fee structure akin to common assets. However, investments that are characterized by longer life cycles, illiquidity, and less transparency, such as private equity, hedge funds, and real estate, often employ performance fees with certain modifications to incentivize managers to act in the best interest of investors.

Let’s consider a private equity fund with a General Partner (GP) who charges a fixed management fee as a percentage of assets under management (AUM) of \(r_m\), beginning-of-period assets of \(P_0\), end-of-period assets of \(P_1\), and a GP performance fee (p) that is a percentage of total return. The GP’s return in currency terms \(R_{GP}\) can be calculated as follows:

$$R_{GP} = (P_1 \times r_m) + max[0, (P_1 – P_0) \times p]$$

The investor’s periodic rate of return, \(r_i\), can be calculated as follows:

$$r_i = \frac{(P_1 – P_0 – R_{GP})}{P_0}$$

Where:

- \(r_i\) = investor’s periodic rate of return
- \(P_1\) = end-of-period assets
- \(P_0\) = beginning-of-period assets
- \(R_{GP}\) = GP’s return in currency terms

GreenWood Hedge Fund has an initial investment capital of $150 million. It charges a 1.5% management fee based on year-end AUM and a 25% performance fee. In its first year, GreenWood generated a 25% return.

Assuming management fees are calculated using an end-of-period valuation, calculate the GP’s return and investor’s return at the end of the first year in the following scenarios:

**Scenario 1: **Performance and management fees are calculated independently:

**Solution**

To determine the GP’s return in currency terms (\( R_{GP} \)) and the investor’s periodic rate of return (\( r_i \)), we proceed as follows:

1. Calculate \( P_1 \) (end-of-period assets):

\[ \begin{align}P_1 &= P_0 \times (1 + \text{return in the first year}\\&= 150 \times 1.25 = \$187.5 \ \text{ million} \end{align}\]

2. Calculate \( R_{GP} \) (GP’s return in currency terms):

\[\begin{align} R_{GP} &= (P_1 \times r_m) + \max[0, (P_1 – P_0) \times p] \\ &= (187.5 \times 0.015) + (37.5 \times 0.25)\\ &= 2.8125 + 9.375 = \$12.1875\ \text{ million} \end{align} \]

3. Calculate \( r_i \) (investor’s periodic rate of return):

\[ \begin{align}r_i &= \frac{(P_1 – P_0 – R_{GP})}{P_0}\\ &= \frac{(187.5 – 150 – 12.1875)}{150} \\ & \approx 0.16875 \ \text{ or }\ 16.875\% \end{align}\]

**Scenario 2: **Performance fee is calculated from the return net of management fee:

In a scenario where the performance fee is calculated from the return net of the management fee, the GP’s return in currency terms (\( R_{GP(Net)} \)) and the investor’s net return (\( r_i \)) under this fee structure, we proceed as follows:

1. Calculate \( R_{GP(Net)} \) (GP’s return considering performance fee net of management fees):

\[ \begin{align}R_{GP(Net)} &= (P_1 \times r_m) + \max\{0, [P_1(1 – r_m) – P_0] \times p\}\\ &= (187.5 \times 0.015) + \max\{0, (187.5 \times 0.985 – 150) \times 0.25\} \\ & \approx \$11.484\ \text{ million}\end{align}\]

2. Calculate \( r_i \) (investor’s net return):

\[ \begin{align}r_i &= \frac{(P_1 – P_0 – R_{GP(Net)})}{P_0}\\ &=\frac{(187.5 – 150 – 11.484}{150}\\ & \approx 17.34\%\end{align} \]

Under this new fee structure for GreenWood Estates:

Intuitively, when performance fees are calculated net of management fees, it reduces the base upon which the performance fee is calculated, leading to a lower total fee for the GP and a slightly higher net return for the investor.

Performance fee modifications can have varying effects on the periodic investor returns depending on the timing of an investment. For instance, in the case of a hard hurdle, both investors would realize a fee reduction equal to \(P_t \times r_h \times p\) (that is, the product of the end-of-period fund value for year t, the hurdle rate, and the performance fee). Nevertheless, in scenarios involving a high-water mark, the fee adjustment’s time-dependent nature produces varying outcomes for an investor who joins the fund at a later stage.

For GreenWood Hedge Fund, assume that an 8% hurdle rate (\( r_h \)) is introduced. Also, the performance fee is calculated from the return net of the management fee.

To determine the GP’s return in currency terms (\( R_{GP(\text{Net with Hurdle})} \)) and the investor’s net return (\( r_i \)) under this fee structure, we proceed as follows:

1. Calculate \( R_{GP(\text{Net with Hurdle})} \) (GP’s return considering performance fee net of management fees and the hurdle rate):

\[\begin{align*}R_{GP(\text{Net with Hurdle})} &= (P_1 \times r_m) + \max\{0, [P_1(1 – r_m) – P_0 \times (1 + r_h)] \times p\}\\

&= (187.5 \times 0.015) + \max\{0, (187.5 \times 0.985 – 150 \times 1.08) \times 0.25\} \\

& \approx \$8.484 \ \text{ million}

\end{align*} \]

2. Calculate \( r_i \) (investor’s net return):

\[ \begin{align}r_i &= \frac{(187.5 – 150 – 8.484}{150} \\ & \approx 19.34\% \end{align}\]

In GreenWood scenario, an 8% hurdle rate meant that only returns above 8% were subject to the 25% performance fee. This structure further reduced the GP’s fee to approximately $8.484 million and increased the net investor return to around 19.34%.

GreenWood Hedge Fund continues its operations into the second year, with its fund value declining to $100 million. Given the previous fee structure (the performance fee is calculated from the return net of the management fee) and the introduction of a high-water mark provision, calculate the GPs return and investors’ return at the in the second year.

To determine the GP’s return in currency terms (\( R_{GP(\text{High-Water Mark})} \)) and the investor’s net return (\( r_i \)) under this fee structure, we proceed as follows:

1. Calculate \( R_{GP(\text{High-Water Mark})} \) (GP’s return considering the high-water mark provision):

\[\begin{align*}

R_{GP(\text{High-Water Mark})} &= (P_2 \times r_m) + \max\{0, (P_2 – P_{HWM}) \times p\} \\

&= (100 \times 0.015) + \max\{0, (100 – (187.5 – 8.484)) \times 0.25\} \\

&= \$1.5\ \text{million}

\end{align*} \]

Note that \(P_{\text{HWM}}\) is defined as the maximum fund value at the end of any previous period net of fees. As such, in this case,

$$P_{\text{HWM}} =187.5 – 8.484=179.016$$

2. Calculate \( r_i \) for the second year (investor’s net return):

\[ \begin{align}r_i &= \frac{(P_2 – P_1 – R_{GP(\text{High-Water Mark})})}{P_1} \\ &=\frac{(100 – 179.016-1.5}{179.016}& \approx -44.98\% \end{align}\]

The investor’s net return for the second year is calculated by considering the decline in the fund’s value and deducting the GP’s fees. The result is a significant negative return because the fund’s value dropped significantly from the high-water mark and was further diminished by the management fee.

The high-water mark provision ensures that the GP doesn’t double-dip by earning fees on the same profits in subsequent periods. It’s a measure to ensure that performance fees are genuinely reflective of the GP’s ability to generate “new” profits above and beyond the highest value the fund has previously achieved.

In some instances, the timing of returns can have a significant impact on manager fees and investor returns. This is particularly evident in the case of a clawback provision. A clawback provision is a contractual clause typically found in private equity and hedge fund structures, which allows for the recovery of money already paid out. If the fund performs well in the early years, the manager may receive a performance fee. However, if the fund subsequently underperforms, the clawback provision ensures that the manager returns the previously paid performance fee, thereby aligning the interests of the manager and the investors.

WestBridge Capital Fund invests $30 million in new ventures, dividing it into two equal parts:

- $15 million into NewtonTech Ltd. (a leveraged buyout).
- $15 million into Electronix Startup (a seed-stage venture).

One year later, NewtonTech was acquired by a larger tech firm for $33 million after costs. Three years later, Electronix Startup undergoes bankruptcy, and WestBridge is unable to recover any of its initial investment. If WestBridge’s fee agreement as a general partner (GP) specifies a 25% performance fee of aggregate profits (p) with a clawback provision, which performance fees will WestBridge accrue, and what will it ultimately receive?

**Solution**

**NewtonTech Investment Return:**

$$\begin{align}\text{Gain }&=\text{Sale Price – Initial Investment}\\& = \$33\ \text{million} – \$15\ \text{million} = \$18\ \text{million}\end{align}$$

**Electronix Startup Investment Loss:**

Loss = $0 – $15 million = -$15 million

**Aggregate Gain of WestBridge after Three Years:**

$$\begin{align}\text{Total Gain}& = \text{Gain from NewtonTech + Loss from Electronix}\\ & = \$18 \ \text{million} – \$15\ \text{million} = \$3\ \text{million}\end{align}$$

**Performance Fee Accrual:**

WestBridge would initially accrue 25% of the $18 million aggregate profit from the sale of NewtonTech at the end of the first year:

Initial Accrued Fee = $18 million × 25% = $4.5 million

This amount is often held in escrow for the benefit of the GP but is not immediately disbursed.

**Adjustment Due to Electronix’s Failure:**

The bankruptcy of Electronix Startup in Year 3 reduces the original $18 million gain by $15 million. Thus, the aggregate fund gain at the end of Year 3 is now only $3 million. This adjusted net profit results in a performance fee of:

Adjusted Fee = $3 million × 25% = $750,000

Due to the clawback provision, WestBridge would then have to return:

$$\begin{align}\text{Return Amount} &= \text{Initial Accrued Fee – Adjusted Fee}\\&= \$4.5\ \text{million} – \$750,000 = \$3.75 \ \text{million}\end{align}$$

This $3.75 million would be returned to Limited Partner (LP) investor capital accounts due to the clawback provision.

WestBridge Capital Fund would ultimately receive a performance fee of $750,000, but it would have to return $3.75 million from the initially accrued fees due to the clawback provision after Electronix Startup’s failure.

Investors who are interested in alternative investments often seek higher risk-adjusted returns that have a low correlation with common asset classes such as stocks and bonds. The performance of these investments, which can range from private equity to real estate, is usually tracked based on relative returns.

In other words, similar to common asset classes, the returns on individual alternative investments are typically compared to a benchmark of investments that have similar features. However, these benchmarks can be interpreted differently or have different characteristics when it comes to alternative investments.

For instance, using a composite benchmark for private equity or real estate investments can be misleading if a specific investment is in a different life cycle phase than most of its peers. To illustrate, consider a private equity investment in a start-up tech company. Comparing its returns to a benchmark that includes mature, established companies would not provide an accurate picture.

More accurate results can be achieved by comparing returns between such investments of the same vintage year on an annual or “since inception” basis. However, factors such as lockups and illiquidity can prevent an investor from reacting to underperformance by selling an investment.

Hedge fund indexes warrant increased scrutiny because of the evolving composition of funds included in a benchmark over time. Research indicates that more than a quarter of all hedge funds experience failure within their initial three years, often as a result of performance issues that result in investor withdrawals and fund closures.

The omission of these failed funds from a particular benchmark can introduce a type of selection bias termed “survivorship bias,” potentially causing investors to develop excessively optimistic return projections. Survivorship bias is a significant issue among hedge fund indexes that only include current investment funds and exclude those funds that are no longer available.

Consider an example where an investor is looking at a hedge fund index that only includes funds that have been successful and excludes those that have failed. The investor might be misled into thinking that investing in hedge funds is a surefire way to make money, not realizing that the index does not include funds that have failed and thus does not accurately represent the risk involved.

Backfill bias relates to the manner and timing of incorporating returns into a benchmark index. For instance, a fund manager might initiate multiple hedge fund investments simultaneously and include only the most prosperous funds in an index a couple of years after their establishment. The subsequent inclusion or “backfilling” of historical performance data selectively can inflate the average reported returns, resulting in what is referred to as backfill bias.

Due to survivorship and backfill biases, benchmark indexes, such as hedge fund indexes, may not accurately reflect the average hedge fund performance but only the returns of those hedge funds that initially performed best and/or have not failed.

QuestionWhich of the following could be the <em>

most likely</em>impact of investor redemptions when a hedge fund is declining in value?

- No significant impact on the hedge fund as it can easily sell assets without incurring any losses or transaction costs.
- Investor redemptions would increase the value of the hedge fund as it would lead to an influx of cash from the sale of assets.
- It could potentially lock in or amplify losses for the hedge fund due to the forced sale of assets at unfavorable prices and additional transaction costs.

The correct answer is C.Investor redemptions could potentially lock in or amplify losses for the hedge fund due to the forced sale of assets at unfavorable prices and additional transaction costs. When a hedge fund is underperforming and investors start redeeming their shares, the fund is forced to sell assets to meet these redemptions. This can lead to a downward spiral, as the fund may have to sell assets at unfavorable prices, thereby locking in losses.<br>

Additionally, the fund incurs transaction costs when selling these assets, which further erodes its value. This situation can be particularly damaging if the fund is invested in illiquid assets that are difficult to sell quickly without incurring significant price discounts. The forced liquidation of assets can also disrupt the fund’s investment strategy and potentially lead to further underperformance. Therefore, investor redemptions can have a significant negative impact on a struggling hedge fund.<br><br>

<b>A is incorrect.</b>This statement is not accurate because selling assets, especially in a distressed situation, often incur transaction costs and can result in selling at unfavorable prices, which can further exacerbate the fund’s losses.<br><br>

<b>B is incorrect.</b>While it’s true that selling assets brings in cash, this does not necessarily increase the value of the hedge fund. If the assets are sold at a loss, the fund’s value will decrease. Furthermore, the influx of cash may be offset by the outflow of cash due to investor redemptions. Therefore, investor redemptions do not necessarily increase the value of the hedge fund.