# Hedge Fund Index Trading Strategies

David Lee

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# Hedge Fund Index Trading Strategies

David Lee

## ABSTRACT

A Hedge Fund Index is an indicator for tracking the performance of hedge fund investments.

The index consists of notional investments in private unregistered Hedge Funds and cash.

Hedge fund index investment also involves re-leveraging and deleveraging. This paper presents a leveraging algorithm for managing the re-leveraging and deleveraging of a hedge fund index. We also propose a method for measuring the performance of hedge fund index.

The model is important given that hedge funds are less transparent and difficult to replicate.

**Key words:** hedge fund index, re-leveraging, deleveraging, index performance, liquidity, exposure.

JEL Classification: E44, G21, G12, G24, G32, G33, G18, G28
# Hedge Fund Index Trading Strategies

David Lee

## ABSTRACT

A Hedge Fund Index is an indicator for tracking the performance of hedge fund investments.

The index consists of notional investments in private unregistered Hedge Funds and cash.

Hedge fund index investment also involves re-leveraging and deleveraging. This paper presents a leveraging algorithm for managing the re-leveraging and deleveraging of a hedge fund index. We also propose a method for measuring the performance of hedge fund index.

The model is important given that hedge funds are less transparent and difficult to replicate.

**Key words:** hedge fund index, re-leveraging, deleveraging, index performance, liquidity, exposure.

JEL Classification: E44, G21, G12, G24, G32, G33, G18, G28
The Hedge Funds of which an index will consist invest in a wide variety of asset worldwide which may include stocks, bonds, currencies, commodities, derivatives, real estate, and private equity. As a general matter, arbitrage funds, also known as reactive value or market neutral funds, seek to exploit price differences among related securities, whereas directional funds use technical and fundamental analysis to make directional investments in a wide array of markets.

Arbitrage funds in which notional investments may be made under the index will employ strategies which may include but are not limited to equity index, merger, statistical equity, fixed income, mortgage-backed securities, and convertible securities arbitrage.

Directional funds in which notional investment may be made under the index may take long or short positions, for instance, on individual equites, bonds, or currencies. In the aggregate notional investments in Hedge Funds under the index will be selected so as to consist of a combination of arbitrage and directional funds with the intention of obtaining stable returns regardless of the performance of equity and fixed income markets

The Index Manager will determine the composition of an Index. The Index will be actively managed by the Index Manager with the intention of accomplishing the Index Return Objective requirements. For instance, one Index Return Objective is to accomplish returns targeted in a range of returns above U.S. treasury bills, annualized standard deviation of less than certain percentage, low correlation to financial markets,
The Hedge Funds of which an index will consist invest in a wide variety of asset worldwide which may include stocks, bonds, currencies, commodities, derivatives, real estate, and private equity. As a general matter, arbitrage funds, also known as reactive value or market neutral funds, seek to exploit price differences among related securities, whereas directional funds use technical and fundamental analysis to make directional investments in a wide array of markets.

Arbitrage funds in which notional investments may be made under the index will employ strategies which may include but are not limited to equity index, merger, statistical equity, fixed income, mortgage-backed securities, and convertible securities arbitrage.

Directional funds in which notional investment may be made under the index may take long or short positions, for instance, on individual equites, bonds, or currencies. In the aggregate notional investments in Hedge Funds under the index will be selected so as to consist of a combination of arbitrage and directional funds with the intention of obtaining stable returns regardless of the performance of equity and fixed income markets

The Index Manager will determine the composition of an Index. The Index will be actively managed by the Index Manager with the intention of accomplishing the Index Return Objective requirements. For instance, one Index Return Objective is to accomplish returns targeted in a range of returns above U.S. treasury bills, annualized standard deviation of less than certain percentage, low correlation to financial markets,
and broad diversification across trading strategies. There is no guarantee that the
aforementioned objective will be accomplished.

There is rich literature on hedge fund investment. Aragon and Nanda (2017) study the hedge fund monthly performance disclosures, and conclude that timely disclosure is an important consideration for hedge fund managers and investors. Atilgan et al (2013) investigate the performance of various hedge fund indices and find that the performance deteriorates over time and conclude that non-investable indices are superior performers with respect to their investable counterparts.

Jackwerth and Slavutskaya (2016) assess the addition of alternative assets to the impact of diversification, addition of positive skewness, and the elimination of left tails of returns on hedge fund investment. Kapil and Gupta (2019) find that most hedge fund indices witness a drop in returns over time, and most hedge funds do not provide additional diversification benefits comparing to traditional asset class.

Honigsberg (2019) shows that measures of misreporting decline after increases in regulation, and this could worsen observed performance. Ardia and Boudt (2018) define a measure of hedge funds and show that the p-values of equal performance can be used to obtain estimates of the hedge fund performance ratio.

McLean and Pontiff (2016) study the out-of-sample and post-publication return predictability of variables shown to predict cross-sectional stock returns. Beschwitz et al (2022) study the
and broad diversification across trading strategies. There is no guarantee that the
aforementioned objective will be accomplished.

There is rich literature on hedge fund investment. Aragon and Nanda (2017) study the hedge fund monthly performance disclosures, and conclude that timely disclosure is an important consideration for hedge fund managers and investors. Atilgan et al (2013) investigate the performance of various hedge fund indices and find that the performance deteriorates over time and conclude that non-investable indices are superior performers with respect to their investable counterparts.

Jackwerth and Slavutskaya (2016) assess the addition of alternative assets to the impact of diversification, addition of positive skewness, and the elimination of left tails of returns on hedge fund investment. Kapil and Gupta (2019) find that most hedge fund indices witness a drop in returns over time, and most hedge funds do not provide additional diversification benefits comparing to traditional asset class.

Honigsberg (2019) shows that measures of misreporting decline after increases in regulation, and this could worsen observed performance. Ardia and Boudt (2018) define a measure of hedge funds and show that the p-values of equal performance can be used to obtain estimates of the hedge fund performance ratio.

McLean and Pontiff (2016) study the out-of-sample and post-publication return predictability of variables shown to predict cross-sectional stock returns. Beschwitz et al (2022) study the
trading activity of fundamental investors and find that hedge funds close their positions too early, thereby forgoing about one-third of the trades' potential profitability.

Stafylas and Anderson (2018) examine hedge fund index construction methodologies, by describing and analyzing case studies and evaluating them using numerical examples. Barth et al. (2021) show that the total returns reported publicly are significantly lower than the returns of funds that report on regulatory filings.

If the Index Manager determines that a Market Disruption Event concerning an investment in a Hedge Fund has occurred and is continuing on any date that but for that event would be a date on which the Index Manager would calculate the index value, then the Index Manager may in its discretion postpone calculation of the index value and the payment of Proceeds at Maturity or Proceeds at Early Redemption until such time as such Market Disruption Event is no longer continuing.

A “Market Disruption Event” is any bona fide event, circumstance or cause (whether or not reasonably foreseeable) beyond the reasonable control of the Index Manager which has or will have a material adverse effect on the ability of the Index Manager to notionally liquidate investments in Hedge Funds in the Index.

This paper proposes a method for measuring hedge fund index performance. The Final Index Value will be equal to the aggregate of the notional liquidation values of all the
trading activity of fundamental investors and find that hedge funds close their positions too early, thereby forgoing about one-third of the trades' potential profitability.

Stafylas and Anderson (2018) examine hedge fund index construction methodologies, by describing and analyzing case studies and evaluating them using numerical examples. Barth et al. (2021) show that the total returns reported publicly are significantly lower than the returns of funds that report on regulatory filings.

If the Index Manager determines that a Market Disruption Event concerning an investment in a Hedge Fund has occurred and is continuing on any date that but for that event would be a date on which the Index Manager would calculate the index value, then the Index Manager may in its discretion postpone calculation of the index value and the payment of Proceeds at Maturity or Proceeds at Early Redemption until such time as such Market Disruption Event is no longer continuing.

A “Market Disruption Event” is any bona fide event, circumstance or cause (whether or not reasonably foreseeable) beyond the reasonable control of the Index Manager which has or will have a material adverse effect on the ability of the Index Manager to notionally liquidate investments in Hedge Funds in the Index.

This paper proposes a method for measuring hedge fund index performance. The Final Index Value will be equal to the aggregate of the notional liquidation values of all the
Hedge Fund comprising the Index including any notional cash in the Index less any accrued Fees and Expenses as of the date of determination.

We use commercially reasonable efforts to determine such notional liquidation value for all Hedge Funds by the Maturity Date or Early Redemption Date; however, it may not be possible to determine such value (see https://finpricing.com/lib/EqWarrant.html) by such date for each and every Hedge Fund in the Index.

To achieve performance objectives, the managers of Hedge Funds will make investments that may be considered speculative and may involve substantial risk of loss. The prices of investments may be highly volatile.

Price movements are influenced by, among other things: changing supply and demand relationships; trade, fiscal, monetary and exchange control hedges; the policies of governments; political and economic events and policies; changes in national and/or international interest rates and rates of inflation; currency devaluations and revaluations; and emotions of the market.

None of these factors can be controlled by the Index Manager or the managers of any of the Hedge Funds and no assurance can be given that and such factors will not affect the performance and returns achieved by the Index.
Hedge Fund comprising the Index including any notional cash in the Index less any accrued Fees and Expenses as of the date of determination.

We use commercially reasonable efforts to determine such notional liquidation value for all Hedge Funds by the Maturity Date or Early Redemption Date; however, it may not be possible to determine such value (see https://finpricing.com/lib/EqWarrant.html) by such date for each and every Hedge Fund in the Index.

To achieve performance objectives, the managers of Hedge Funds will make investments that may be considered speculative and may involve substantial risk of loss. The prices of investments may be highly volatile.

Price movements are influenced by, among other things: changing supply and demand relationships; trade, fiscal, monetary and exchange control hedges; the policies of governments; political and economic events and policies; changes in national and/or international interest rates and rates of inflation; currency devaluations and revaluations; and emotions of the market.

None of these factors can be controlled by the Index Manager or the managers of any of the Hedge Funds and no assurance can be given that and such factors will not affect the performance and returns achieved by the Index.
The strategies employed by the managers of Hedge Funds may require frequent trading. Therefore, brokerage commission expenses incurred by Hedge Funds may vastly exceed those of other trading entities of comparable size, and affect the Hedge Funds' earnings and in turn the performance of the Index. Costs, fees and expenses incurred by Hedge Funds in which investments are made under the Index will affect the individual returns or losses experienced by such Hedge Funds, and thus the returns or losses generated under the Index.

Index may effectively be leveraged from time to time as determined by the Index Manager through the use of Notional Borrowings. The Index Manager also may effectively Re-leverage or Deleverage the Index from time to time to balance the Leverage Ratio Leveraging and Re-leveraging the Index will result in Notional Borrowing Fees.

We propose a leveraging algorithm that helps to determine hedge fund index re-leveraging or deleveraging. Interest rates will have an effect upon the timing of any Re-leveraging and Deleveraging.

In general, a rise in interest rates will cause the Net Present Value to decrease, and thereby, the Leverage Ratio to decrease, thus, increasing the likelihood of a Re-leveraging. Likewise, a decline in interest rates will in general cause the Net Present Value to increase, and thereby, the Leverage Ratio to increase, thus, increasing the likelihood of a Deleveraging.
The strategies employed by the managers of Hedge Funds may require frequent trading. Therefore, brokerage commission expenses incurred by Hedge Funds may vastly exceed those of other trading entities of comparable size, and affect the Hedge Funds' earnings and in turn the performance of the Index. Costs, fees and expenses incurred by Hedge Funds in which investments are made under the Index will affect the individual returns or losses experienced by such Hedge Funds, and thus the returns or losses generated under the Index.

Index may effectively be leveraged from time to time as determined by the Index Manager through the use of Notional Borrowings. The Index Manager also may effectively Re-leverage or Deleverage the Index from time to time to balance the Leverage Ratio Leveraging and Re-leveraging the Index will result in Notional Borrowing Fees.

We propose a leveraging algorithm that helps to determine hedge fund index re-leveraging or deleveraging. Interest rates will have an effect upon the timing of any Re-leveraging and Deleveraging.

In general, a rise in interest rates will cause the Net Present Value to decrease, and thereby, the Leverage Ratio to decrease, thus, increasing the likelihood of a Re-leveraging. Likewise, a decline in interest rates will in general cause the Net Present Value to increase, and thereby, the Leverage Ratio to increase, thus, increasing the likelihood of a Deleveraging.
The rest of this paper is organized as follows: Hedge fund trading strategies are discussed in Section 1; Section 2 describes hedge fund index behaviors. Index re-leveraging and deleveraging are explained in Section 3; the conclusions are given in Section 4.

# 1. Hedge Fund Trading Strategies

Hedge fund index performance is significantly impacted by hedge fund trading strategies. The following describes various trading strategies of the Hedge Funds which may form part of an Index. There may be additional types of trading strategies that will be part of the Index which are not described herein.

Convertible securities arbitrage takes advantage of a mispricing between a convertible security, such as a bond convertible into common stock, and its theoretical fair value. For example, a hedge fund might purchase an undervalued convertible bond and then hedge it by short selling the underlying stock attempting to lock in a profit. This strategy is implemented on convertible securities issued worldwide and may include securities issued by U.S., European and Asian issuers.

Statistical arbitrage funds use mathematical models and formulas to create portfolios of undervalued and overvalued stocks as measured by various factors. They then would buy the undervalued stocks and sell short the overvalued stocks. They also may seek to
The rest of this paper is organized as follows: Hedge fund trading strategies are discussed in Section 1; Section 2 describes hedge fund index behaviors. Index re-leveraging and deleveraging are explained in Section 3; the conclusions are given in Section 4.

# 1. Hedge Fund Trading Strategies

Hedge fund index performance is significantly impacted by hedge fund trading strategies. The following describes various trading strategies of the Hedge Funds which may form part of an Index. There may be additional types of trading strategies that will be part of the Index which are not described herein.

Convertible securities arbitrage takes advantage of a mispricing between a convertible security, such as a bond convertible into common stock, and its theoretical fair value. For example, a hedge fund might purchase an undervalued convertible bond and then hedge it by short selling the underlying stock attempting to lock in a profit. This strategy is implemented on convertible securities issued worldwide and may include securities issued by U.S., European and Asian issuers.

Statistical arbitrage funds use mathematical models and formulas to create portfolios of undervalued and overvalued stocks as measured by various factors. They then would buy the undervalued stocks and sell short the overvalued stocks. They also may seek to
maintain a neutral posture with respect to numerous risk factors, such as market
exposure, industry and sector exposure, and beta. This strategy generally is associated
with a high frequency of trading as the portfolios are continually rebalanced to maintain
optimal positions. Statistical arbitrage is typically implemented on stocks traded in the
U.S., European, and Pacific Rim markets.

Equity index arbitrage seeks to exploit price differences between stock index futures and the underlying stocks from which the futures price is determined. For example, a hedge fund engaging in S&P 500® Index arbitrage would look for disparities between the price of the S&P 500® futures contract and the stocks comprising the S&P 500® Index. For example, if the S&P 500® futures contract is trading below its “fair value”, then a hedge fund could buy the S&P 500 futures contract and simultaneously sell the underlying stocks that make up the S&P 500 to make an arbitrage profit.

Merger arbitrage attempts to capitalize on price differences in the market between the proposed terms of a merger and the current market prices of the stocks involved. For example, in a one-for-one share exchange, if the acquirer's stock were trading at $50 per share and the target company were trading at $40 per share, a merger arbitrageur would attempt to lock in a $10 profit. This could be done by purchasing shares of the target company and then short selling an equal number of shares of the acquirer. Merger arbitrage trading strategies are practised in equity markets worldwide.
maintain a neutral posture with respect to numerous risk factors, such as market
exposure, industry and sector exposure, and beta. This strategy generally is associated
with a high frequency of trading as the portfolios are continually rebalanced to maintain
optimal positions. Statistical arbitrage is typically implemented on stocks traded in the
U.S., European, and Pacific Rim markets.

Equity index arbitrage seeks to exploit price differences between stock index futures and the underlying stocks from which the futures price is determined. For example, a hedge fund engaging in S&P 500® Index arbitrage would look for disparities between the price of the S&P 500® futures contract and the stocks comprising the S&P 500® Index. For example, if the S&P 500® futures contract is trading below its “fair value”, then a hedge fund could buy the S&P 500 futures contract and simultaneously sell the underlying stocks that make up the S&P 500 to make an arbitrage profit.

Merger arbitrage attempts to capitalize on price differences in the market between the proposed terms of a merger and the current market prices of the stocks involved. For example, in a one-for-one share exchange, if the acquirer's stock were trading at $50 per share and the target company were trading at $40 per share, a merger arbitrageur would attempt to lock in a $10 profit. This could be done by purchasing shares of the target company and then short selling an equal number of shares of the acquirer. Merger arbitrage trading strategies are practised in equity markets worldwide.
Fixed income arbitrage funds generally engage in matched purchase and sale, or sale and purchase transactions in the same or similar fixed income instruments using strategies which include basis trading, calendar spread trading, yield curve arbitrage, intermarket spread trading and rate cap hedging. For example, basis trading involves the purchase or sale of a derivative instrument and the offsetting purchase or sale of the corresponding cash market instrument. Calendar spread trading involves the purchase or sale of a futures contract for delivery of a fixed income commodity in a given month and the opposite sale or purchase of a futures contract for delivery of the same commodity in a different month.

Mortgage-backed securities arbitrage attempts to take advantage of mispricings in the mortgage-backed securities market. Opportunities arise in the mortgage-backed securities markets when the price of a mortgage-backed security inaccurately reflects the true default risk or prepayment risk of the mortgages securing the underlying issue. An index of the mispriced securities is traded and then hedged using other mortgage-backed securities, U.S. Treasury securities, and interest rate futures with the intention of removing the market risk and leaving an above market return.

Equity long/short, also known as equity hedged, seeks to profit through successful stock selection which is generally based upon fundamental analysis and research. Hedge funds engaged in this strategy will maintain both long and short positions in individual stocks as well as stock indices. These funds typically maintain a net long market exposure ranging between 10% to 80% of capital but can also be net short at times. Most funds in
Fixed income arbitrage funds generally engage in matched purchase and sale, or sale and purchase transactions in the same or similar fixed income instruments using strategies which include basis trading, calendar spread trading, yield curve arbitrage, intermarket spread trading and rate cap hedging. For example, basis trading involves the purchase or sale of a derivative instrument and the offsetting purchase or sale of the corresponding cash market instrument. Calendar spread trading involves the purchase or sale of a futures contract for delivery of a fixed income commodity in a given month and the opposite sale or purchase of a futures contract for delivery of the same commodity in a different month.

Mortgage-backed securities arbitrage attempts to take advantage of mispricings in the mortgage-backed securities market. Opportunities arise in the mortgage-backed securities markets when the price of a mortgage-backed security inaccurately reflects the true default risk or prepayment risk of the mortgages securing the underlying issue. An index of the mispriced securities is traded and then hedged using other mortgage-backed securities, U.S. Treasury securities, and interest rate futures with the intention of removing the market risk and leaving an above market return.

Equity long/short, also known as equity hedged, seeks to profit through successful stock selection which is generally based upon fundamental analysis and research. Hedge funds engaged in this strategy will maintain both long and short positions in individual stocks as well as stock indices. These funds typically maintain a net long market exposure ranging between 10% to 80% of capital but can also be net short at times. Most funds in
the category are generalists in that they invest in stocks across a broad range of sectors
while others focus on one particular sector of the market.

Short selling funds engage in the shorting of stocks in an attempt to profit from declines
in the prices of those stocks. These short positions are typically established based on
fundamental analysis and research. Short funds may also have some long positions in
their portfolios but will maintain an overall net short exposure to the market.

Macro funds trade in all types of assets classes on a global basis, including currencies,
equities, fixed income, commodities and derivatives. These funds attempt to identify
macroeconomic themes occurring in the global marketplace and seek to profit by
establishing positions in various securities which will either benefit or suffer from such
trends. Their ability to generate profits is dependent upon their skill in identifying these
trends before the rest of the market.

## 2. Hedge Fund Index Behaviours

Hedge fund indices are well known for representing the performance of the hedge fund industry. In order for hedge funds to appreciate over its term, the Index components (i.e., the Hedge Funds and any cash) will have to generate a positive return, assuming no Notional Borrowings.
the category are generalists in that they invest in stocks across a broad range of sectors
while others focus on one particular sector of the market.

Short selling funds engage in the shorting of stocks in an attempt to profit from declines
in the prices of those stocks. These short positions are typically established based on
fundamental analysis and research. Short funds may also have some long positions in
their portfolios but will maintain an overall net short exposure to the market.

Macro funds trade in all types of assets classes on a global basis, including currencies,
equities, fixed income, commodities and derivatives. These funds attempt to identify
macroeconomic themes occurring in the global marketplace and seek to profit by
establishing positions in various securities which will either benefit or suffer from such
trends. Their ability to generate profits is dependent upon their skill in identifying these
trends before the rest of the market.

## 2. Hedge Fund Index Behaviours

Hedge fund indices are well known for representing the performance of the hedge fund industry. In order for hedge funds to appreciate over its term, the Index components (i.e., the Hedge Funds and any cash) will have to generate a positive return, assuming no Notional Borrowings.
In the event there are Notional Borrowings, it would be necessary for the Index to generate an additional positive return equal to approximately one-month U.S. dollar London Inter-Bank Offer Rate (LIBOR) plus a spread on the amount of the Notional Borrowings.

Hedge fund investment also provide additional diversification across Hedge Funds.

Rather than having exposure to only one or a few hedge fund managers and strategies, the investment is exposed to the performance of numerous funds among a wide array of trading strategies.

Although the Index Manager anticipates that the Index generally shall consist of at least 15 different Hedge Funds, there is no requirement to maintain any minimum number of Hedge Funds in the Index. Consequently, the benefits of diversification are expected but cannot be guaranteed.

The returns provided by a basket of Hedge Funds generally would have been more stable on a historical basis as compared to many other traditional investment strategies. Stability is commonly judged by the range of returns experienced over a period of time. One measure of this range is referred to as the standard deviation of returns.

The smaller the standard deviation, the narrower the range and the more stable the past returns. Generally, a low standard deviation of previous returns is significant because it is an indicator of lower risk. Historically, hedge funds have had a low standard deviation as
In the event there are Notional Borrowings, it would be necessary for the Index to generate an additional positive return equal to approximately one-month U.S. dollar London Inter-Bank Offer Rate (LIBOR) plus a spread on the amount of the Notional Borrowings.

Hedge fund investment also provide additional diversification across Hedge Funds.

Rather than having exposure to only one or a few hedge fund managers and strategies, the investment is exposed to the performance of numerous funds among a wide array of trading strategies.

Although the Index Manager anticipates that the Index generally shall consist of at least 15 different Hedge Funds, there is no requirement to maintain any minimum number of Hedge Funds in the Index. Consequently, the benefits of diversification are expected but cannot be guaranteed.

The returns provided by a basket of Hedge Funds generally would have been more stable on a historical basis as compared to many other traditional investment strategies. Stability is commonly judged by the range of returns experienced over a period of time. One measure of this range is referred to as the standard deviation of returns.

The smaller the standard deviation, the narrower the range and the more stable the past returns. Generally, a low standard deviation of previous returns is significant because it is an indicator of lower risk. Historically, hedge funds have had a low standard deviation as
compared to other investments. The Index Return Objective seeks to maintain a standard
deviation of less than 7%, however, such a deviation cannot be guaranteed.

The index return for month m is given by:

$$
\kappa_m = \sum_i \omega_m^{bi} \rho_m^i - \phi. \tag{1}
$$

The weight at the end of the month is also calculated in the as:

$$
\omega_m^{ei} = \frac{1 + \rho_m^i}{1 + \kappa_m + \phi} \omega_m^{bi}. \tag{2}
$$

where $\omega_m^b$ is the fund weight at the beginning of a month, $\rho_m^i$ is the return of fund i in month m, and $\phi$ is the accrual fee.

On an interim valuation basis, the Index Manager will determine the Index Value based
upon the aggregate of the net asset values of all the notional investments in Hedge Funds
comprising the Index including any notional cash in the Index less any accrued Fees and
Expenses as of the date of determination.

The net asset values used by the Index Manager will be based upon information provided
by the Hedge Funds or each fund's respective administrator or accountant. If such
compared to other investments. The Index Return Objective seeks to maintain a standard
deviation of less than 7%, however, such a deviation cannot be guaranteed.

The index return for month m is given by:

$$
\kappa_m = \sum_i \omega_m^{bi} \rho_m^i - \phi. \tag{1}
$$

The weight at the end of the month is also calculated in the as:

$$
\omega_m^{ei} = \frac{1 + \rho_m^i}{1 + \kappa_m + \phi} \omega_m^{bi}. \tag{2}
$$

where $\omega_m^b$ is the fund weight at the beginning of a month, $\rho_m^i$ is the return of fund i in month m, and $\phi$ is the accrual fee.

On an interim valuation basis, the Index Manager will determine the Index Value based
upon the aggregate of the net asset values of all the notional investments in Hedge Funds
comprising the Index including any notional cash in the Index less any accrued Fees and
Expenses as of the date of determination.

The net asset values used by the Index Manager will be based upon information provided
by the Hedge Funds or each fund's respective administrator or accountant. If such
information is not available on a timely basis for any reason, then the values will be
based upon verbal estimates provided by the manager of each Hedge Fund.

The Index Manager may establish its own net asset value for a Hedge Fund in the Index
in the event a valuation is not available from the administrator, accountant or manager, or
if the Index Manager has reason to believe such valuation provided by the administrator,
accountant, or manager is not accurate.

The Index Manager may update previously made valuations of a Hedge Fund from time
to time upon receipt of updated or revised information. Accordingly, index investment at
the determination date may be less than or greater than the amount which may be
determined at a subsequent time.

In the event that the Index Manager in its sole discretion cannot determine the
liquidation value of any of the Hedge Funds in the Index as of the Maturity Date or the
Early Redemption Date, Index manager may withhold payment to investors of that
portion of the Proceeds at Maturity or Proceeds at Early Redemption in excess of the
Deposit Amount until such Pending Liquidation Amount has been determined.

3. Re-leveraging and Deleveraging
information is not available on a timely basis for any reason, then the values will be
based upon verbal estimates provided by the manager of each Hedge Fund.

The Index Manager may establish its own net asset value for a Hedge Fund in the Index
in the event a valuation is not available from the administrator, accountant or manager, or
if the Index Manager has reason to believe such valuation provided by the administrator,
accountant, or manager is not accurate.

The Index Manager may update previously made valuations of a Hedge Fund from time
to time upon receipt of updated or revised information. Accordingly, index investment at
the determination date may be less than or greater than the amount which may be
determined at a subsequent time.

In the event that the Index Manager in its sole discretion cannot determine the
liquidation value of any of the Hedge Funds in the Index as of the Maturity Date or the
Early Redemption Date, Index manager may withhold payment to investors of that
portion of the Proceeds at Maturity or Proceeds at Early Redemption in excess of the
Deposit Amount until such Pending Liquidation Amount has been determined.

3. Re-leveraging and Deleveraging
Contingent upon positive performance of the Index, investment may involve deleveraging: Notional Borrowings that effectively will permit additional leverage of the Deposit Amount for a total of 100% of the Deposit Amount, or $1,000 of Notional Borrowings for every $1,000 of Deposit Amount initially invested. This effective extension of leverage may exceed 100% of the Deposit Amount and is completely contingent upon appreciation of the Index.

On each day, the Index Manager will determine the Leverage Ratio inherent in the Index as defined by the following formula:

$$Leverage Ratio = \frac{\text{Hedge Fund Balance}}{\text{Value} - \text{Net Present Value}}$$

where: “**Hedge Fund Balance**” equals the aggregate value of the notional investments in Hedge Funds in the Index (excluding notional cash) and “**Net Present Value**” is the present value of the aggregate Deposit Amount to be paid on the Maturity Date discounted at the prevailing applicable zero-coupon discount rate.

Deleveraging may occur each time the Leverage Ratio falls below a threshold and deleveraging may occur each time the Leverage Ratio rises above another threshold.

All examples used are for illustrative purposes only and should not be relied upon as estimates, forecasts or projections for the investment or the performance of the Index. For simplicity, the following examples assume an aggregate Deposit Amount of $1,000.
Contingent upon positive performance of the Index, investment may involve deleveraging: Notional Borrowings that effectively will permit additional leverage of the Deposit Amount for a total of 100% of the Deposit Amount, or $1,000 of Notional Borrowings for every $1,000 of Deposit Amount initially invested. This effective extension of leverage may exceed 100% of the Deposit Amount and is completely contingent upon appreciation of the Index.

On each day, the Index Manager will determine the Leverage Ratio inherent in the Index as defined by the following formula:

$$Leverage Ratio = \frac{Hedge Fund Balance}{Value - Net Present Value}$$

where: “**Hedge Fund Balance**” equals the aggregate value of the notional investments in Hedge Funds in the Index (excluding notional cash) and “**Net Present Value**” is the present value of the aggregate Deposit Amount to be paid on the Maturity Date discounted at the prevailing applicable zero-coupon discount rate.

Deleveraging may occur each time the Leverage Ratio falls below a threshold and deleveraging may occur each time the Leverage Ratio rises above another threshold.

All examples used are for illustrative purposes only and should not be relied upon as estimates, forecasts or projections for the investment or the performance of the Index. For simplicity, the following examples assume an aggregate Deposit Amount of $1,000.
As an example of the Leverage Ratio calculation, if the Net Present Value is $750, the Value is $1,000 and the Hedge Fund Balance is $1,000, then the Leverage Ratio will be 4.00. This is calculated as follows:

$$4.00 = \frac{\$1,000}{\$1,000 - \$750}$$

Over time, the Net Present Value will gradually rise to $1,000 by the Maturity Date reflecting the aggregate Deposit Amount of $1,000 as used in these examples (but will increase and/or decrease according to changes in interest rates). However, as the Index generates profits, the Hedge Fund Balance and the Value may increase. If the Leverage Ratio falls below 3.50, Index manger effectively will inject sufficient additional capital into the Index (the “Notional Borrowings”) to return the Leverage Ratio to approximately 4.00.

For example, with the Hedge Fund Balance at $1,150, the Value at $1,150, and assuming that by this time the Net Present Value has increased to $800, then the Leverage Ratio would be 3.28 according to the formula:

$$3.28 = \frac{\$1,150}{\$1,150 - \$800}$$
As an example of the Leverage Ratio calculation, if the Net Present Value is $750, the Value is $1,000 and the Hedge Fund Balance is $1,000, then the Leverage Ratio will be 4.00. This is calculated as follows:

$$4.00 = \frac{\$1,000}{\$1,000 - \$750}$$

Over time, the Net Present Value will gradually rise to $1,000 by the Maturity Date reflecting the aggregate Deposit Amount of $1,000 as used in these examples (but will increase and/or decrease according to changes in interest rates). However, as the Index generates profits, the Hedge Fund Balance and the Value may increase. If the Leverage Ratio falls below 3.50, Index manger effectively will inject sufficient additional capital into the Index (the “Notional Borrowings”) to return the Leverage Ratio to approximately 4.00.

For example, with the Hedge Fund Balance at $1,150, the Value at $1,150, and assuming that by this time the Net Present Value has increased to $800, then the Leverage Ratio would be 3.28 according to the formula:

$$3.28 = \frac{\$1,150}{\$1,150 - \$800}$$
Since the Leverage Ratio is below the “Re-leveraging” trigger of 3.50, The Index Manager will increase leverage through the use of Notional Borrowings bringing it to approximately 4.00. In this example, the Hedge Fund Balance would be increased by $250 to $1,400. Notional Borrowings would now total 25% of the Deposit Amount.

$$4.00 = \frac{\$1,400}{\$1,150 - \$800}$$

In the event that the Value declines or the Net Present Value rises, this will cause the Leverage Ratio to rise. Every time the Leverage Ratio rises above 5.00, the Index Manager may “Deleverage” the Index by converting a portion of the Hedge Funds to cash, in an amount such that the Leverage Ratio is restored to approximately 4.75.

Using the previous example as a starting point, a loss of 10% would cause the Hedge Fund Balance to fall from $1,400 to $1,260, the Value to fall from $1,150 to approximately $1,010, and the Leverage Ratio to rise to 6.00 as shown:

$$6.00 = \frac{\$1,260}{\$1,010 - \$800}$$

This would trigger a Deleveraging, and fund owner would have the right to request that the Index Manager decrease leverage to 4.00. In this example, $420 worth of notional investments in Hedge Funds would be liquidated and held as cash, which would reduce the Hedge Fund Balance from $1,260 to $840.
Since the Leverage Ratio is below the “Re-leveraging” trigger of 3.50, The Index Manager will increase leverage through the use of Notional Borrowings bringing it to approximately 4.00. In this example, the Hedge Fund Balance would be increased by $250 to $1,400. Notional Borrowings would now total 25% of the Deposit Amount.

$$4.00 = \frac{\$1,400}{\$1,150 - \$800}$$

In the event that the Value declines or the Net Present Value rises, this will cause the Leverage Ratio to rise. Every time the Leverage Ratio rises above 5.00, the Index Manager may “Deleverage” the Index by converting a portion of the Hedge Funds to cash, in an amount such that the Leverage Ratio is restored to approximately 4.75.

Using the previous example as a starting point, a loss of 10% would cause the Hedge Fund Balance to fall from $1,400 to $1,260, the Value to fall from $1,150 to approximately $1,010, and the Leverage Ratio to rise to 6.00 as shown:

$$6.00 = \frac{\$1,260}{\$1,010 - \$800}$$

This would trigger a Deleveraging, and fund owner would have the right to request that the Index Manager decrease leverage to 4.00. In this example, $420 worth of notional investments in Hedge Funds would be liquidated and held as cash, which would reduce the Hedge Fund Balance from $1,260 to $840.
$$4.00 = \frac{\$840}{\$1,010 - \$800}$$

This example illustrates that if the Index incurs significant losses, the leveraging algorithm will eventually cause the Hedge Fund Balance to fall to zero, at which point the Index would be entirely allocated to cash.

## 4. Conclusion

This article presents a model for measuring hedge fund index and conducting index re-leveraging and deleveraging. Performance also will determine whether or not the Index Manager will affect a Deleveraging. In order to avoid a Deleveraging, the Index would have to generate a positive return in excess of the Fees and Expenses of the Index, the rate of increase in the Net Present Value as well as the effect of any decline in interest rates.

By holding a hedge fund index associated investment, an investor can maintain a potential for generating higher returns than traditional fixed income securities as well as diversifying into alternative asset classes. The investment may provide a market neutral holding with minimal correlation to equity and bond markets, that can generate positive returns in both rising and falling markets.
$$4.00 = \frac{\$840}{\$1,010 - \$800}$$

This example illustrates that if the Index incurs significant losses, the leveraging algorithm will eventually cause the Hedge Fund Balance to fall to zero, at which point the Index would be entirely allocated to cash.

## 4. Conclusion

This article presents a model for measuring hedge fund index and conducting index re-leveraging and deleveraging. Performance also will determine whether or not the Index Manager will affect a Deleveraging. In order to avoid a Deleveraging, the Index would have to generate a positive return in excess of the Fees and Expenses of the Index, the rate of increase in the Net Present Value as well as the effect of any decline in interest rates.

By holding a hedge fund index associated investment, an investor can maintain a potential for generating higher returns than traditional fixed income securities as well as diversifying into alternative asset classes. The investment may provide a market neutral holding with minimal correlation to equity and bond markets, that can generate positive returns in both rising and falling markets.
In order to avoid a Deleveraging, the Index would have to generate a positive gain in excess of the Fees and Expenses of the Index, the rate of increase in the Net Present Value (equal to approximately 5.75% per annum), as well as the effect of any decline in interest rates.

References:

Aragon, G. and V. Nanda (2017). Strategic delays and clustering in hedge fund reported returns. Journal of Financial and Quantitative Analysis 52, 1-35.

Ardia, D. and K. Boudt (2018), “The Peer Performance Ratios of Hedge Funds”, Journal of Banking & Finance, 87, 351-368.

Atilgan, Y., Bali, T., and Demirtas, K., (2013), The performance of hedge fund indices, Borsa Istanbul Review, 13 (3), 30-52.

Aragon, G. and V. Nanda (2017). Strategic delays and clustering in hedge fund reported returns. Journal of Financial and Quantitative Analysis 52, 1-35.

Barth, D., J. Joenväärä, M. Kauppila, and R. Wermers (2021). “The hedge fund industry is bigger (and has performed better) than you think.” Working paper, Office of Financial Research.
In order to avoid a Deleveraging, the Index would have to generate a positive gain in excess of the Fees and Expenses of the Index, the rate of increase in the Net Present Value (equal to approximately 5.75% per annum), as well as the effect of any decline in interest rates.

References:

Aragon, G. and V. Nanda (2017). Strategic delays and clustering in hedge fund reported returns. Journal of Financial and Quantitative Analysis 52, 1-35.

Ardia, D. and K. Boudt (2018), “The Peer Performance Ratios of Hedge Funds”, Journal of Banking & Finance, 87, 351-368.

Atilgan, Y., Bali, T., and Demirtas, K., (2013), The performance of hedge fund indices, Borsa Istanbul Review, 13 (3), 30-52.

Aragon, G. and V. Nanda (2017). Strategic delays and clustering in hedge fund reported returns. Journal of Financial and Quantitative Analysis 52, 1-35.

Barth, D., J. Joenväärä, M. Kauppila, and R. Wermers (2021). “The hedge fund industry is bigger (and has performed better) than you think.” Working paper, Office of Financial Research.
Beschwitz, B., S. Lunghi, and D. Schmidt, 2022, Fundamental arbitrage under the microscope: evidence from detailed hedge fund transaction data, The Review of Asset Pricing Studies, 12 (1), 199-242.

Choi, James J and Kevin Zhao (2020). "Did Mutual Fund Return Persistence Persist? Working Paper 26707." National Bureau of Economic Research.

Dimmock, S., and W. Gerken (2016). "Regulatory oversight and return misreporting by hedge funds." Review of Finance 20, 795-821.

Honigsberg, C. (2019). "Hedge fund regulation and fund governance: Evidence on the effects of mandatory disclosure rules." Journal of Accounting Research 57, 845-888.

Jackwerth, J. and I. Slavutskaya (2016). The total benefit of alternative assets to pension fund portfolios. Journal of Financial Markets 31, 25-42.

Kapil, S. and J. Gupta (2019), Performance Characteristics of Hedge Fund Indices, Theoretical Economics Letters, 9 (6), 2176-2197.

McLean, R. and J. Pontiff (2016). Does academic publication destroy stock return predictability? Journal of Finance 71, 5-32.
Beschwitz, B., S. Lunghi, and D. Schmidt, 2022, Fundamental arbitrage under the microscope: evidence from detailed hedge fund transaction data, The Review of Asset Pricing Studies, 12 (1), 199-242.

Choi, James J and Kevin Zhao (2020). "Did Mutual Fund Return Persistence Persist? Working Paper 26707." National Bureau of Economic Research.

Dimmock, S., and W. Gerken (2016). "Regulatory oversight and return misreporting by hedge funds." Review of Finance 20, 795-821.

Honigsberg, C. (2019). "Hedge fund regulation and fund governance: Evidence on the effects of mandatory disclosure rules." Journal of Accounting Research 57, 845-888.

Jackwerth, J. and I. Slavutskaya (2016). The total benefit of alternative assets to pension fund portfolios. Journal of Financial Markets 31, 25-42.

Kapil, S. and J. Gupta (2019), Performance Characteristics of Hedge Fund Indices, Theoretical Economics Letters, 9 (6), 2176-2197.

McLean, R. and J. Pontiff (2016). Does academic publication destroy stock return predictability? Journal of Finance 71, 5-32.
Stafylas, D. and K. Anderson, 2018, Hedge fund index-engineering methodologies: a comparison and demonstration, Applied Economics, 50 (6), 596-612.
Stafylas, D. and K. Anderson, 2018, Hedge fund index-engineering methodologies: a comparison and demonstration, Applied Economics, 50 (6), 596-612.