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# Fund Management

After completing this reading, you should be able to:

• Differentiate among open-end mutual funds, closed-end mutual funds, and exchange-traded funds (ETFs).
• Calculate the net asset value (NAV) of an open-end mutual fund.
• Understand the various potential undesirable behaviors in trading at mutual funds.
• Explain the key differences between hedge funds and mutual funds.
• Calculate the return on a hedge fund investment and explain the incentive fee structure of a hedge fund, including the terms hurdle rate, high-water mark, and clawback.
• Describe various hedge fund strategies, including long/short equity, dedicated short, distressed securities, merger arbitrage, convertible arbitrage, fixed income arbitrage, emerging markets, global macro, and managed futures, and identify the risks faced by hedge funds.
• Describe characteristics of mutual fund and hedge fund performance and explain the effect of measurement biases on performance measurement.

## Fund Managers

Fund managers are responsible for investing funds on behalf of their clients, based on clients’ investment goals and risk appetites. The benefits of using fund managers include:

1. Fund managers have the necessary expertise needed to invest funds;
2. Large funds make it easier for diversification as opposed to smaller funds or when investors invest on their own;
3. Transacting larger trades is relatively cheaper than transacting smaller ones.

## Mutual Funds

A mutual fund is made up of a pool of money collected from many investors. The money is then used to invest in securities such as stocks and bonds. The funds are operated by a fund manager whose mandate is to generate income or capital gains. However, mutual funds lack tax benefits, meaning that an investor’s profits are subject to being taxed.

A mutual fund can be open-end or closed-end.

### Open-End Mutual Fund

In an open-end mutual fund, shares are traded at their net asset value (NAV). The net asset value is the market value of all assets the fund owns at the end of each trading day minus liabilities divided by the number of shares outstanding., i.e.,

$$NAV=\frac{\text{Market value of assets at the close of the day}- \text{Liabilities}}{\text{Number of outstanding shares}}$$

The net asset value (NAV) changes on a daily basis, usually at 4 pm every day, to reflect changes in the underlying investments, which are usually stocks and bonds. All shares are also purchased or redeemed at the NAV. In an open-end fund, one deals with the fund itself when buying shares.

The open-end mutual funds can be further divided into:

• Money Market funds
• Bonds funds
• Equity funds

The funds that invest in more than one security are termed hybrid funds or multi-asset funds.

#### Money Market Funds

In money market funds, the fund manager invests in fixed income securities with a maturity period of less than a year. These act as an alternative to savings accounts in a bank since they usually offer higher interest rates than a bank savings account.

#### Bond Funds

These funds invest in fixed-income securities with a maturity period greater than a year.

#### Equity Funds

These funds can either be actively managed funds (where investors apply their expertise to achieve the objectives of the fund) or index funds (where the equities track a specific fund, for example, the FTSE 100).

To determine how well a fund has tracked its intended index, tracking error is applied. The most popular tracking area involves obtaining the mean square error, i.e., the squared root of the mean squared difference between the return of the funds and the index (hence the tracking error is also called root-mean-square error).

Example: Calculating the Tracking Error of Index Fund

The 5-year successive returns for FTSE100 are 3%, 10%, 11%, -7% and 4.0%. The respective returns on the fund is 3.0%. 9%, 10%, -5% and 4.0%. What is the tracking error of the fund?

Solution

\begin{align} \text{Tracking Error} &=\sqrt{\frac{\left(3\%-3\%\right)^2+\left(10\%-9\%\right)^2+\left(11\%-10\%\right)^2+\left(-7\%+5\%\right)^2+\left(4.0\%-4.0\%\right)^2}{5}}\\ &=1.10\% \end{align}

## The Expense Ratio

The cost ratio is the annual management fee expressed as a percentage of the assets’ value under management. Other expenses charged on the mutual funds are the front-end load, which is the fee charged on mutual fund investors when they buy, and back-load, which is the fee charged on the investors when they sell.

## Closed-End Mutual Funds

In closed-end funds, the number of shares is constant throughout the time. In other words, the number of shares in a closed-end fund does not change on a daily basis. Shares are publicly traded on an exchange, and therefore the price is a function of supply and demand. Shares are bought and sold through brokers. After the initial share sale, no more shares are issued.

#### Differences Between Open-End and Closed-End Mutual Funds

$$\begin{array}{l|l|l} \textbf{Basis for Comparison} & \textbf{Open-end Funds} & \textbf{Closed-end Funds} \\ \hline \text{Subscription} & \text{Available for subscription} & \text{Available for subscription only} \\ {} & \text{throughout the year.} & \text{during a few specified days.} \\ \hline \text{Listing} & \text{Not listed on a stock exchange.} & \text{Listed on an exchange for} \\ {} & \text{Transactions occur directly} & \text{trading.} \\ {} & \text{through the fund.} & {} \\ \hline \text{Transactions} & \text{Executed at the end of the day.} & \text{Executed in real time.} \\ \hline \text{Maturity} & \text{No fixed maturity.} & \text{Fixed maturity period, say, 3-5} \\ {} & {} & \text{years.} \\ \hline \text{Selling price} & \text{NAV.} & \text{Premium/discount to NAV.} \\ \hline \text{Corpus} & \text{Variable.} & \text{Fixed.} \\ \end{array}$$

Exchange-traded funds combine the features of both open and closed-ended mutual funds. To create an ETF, an investor deposits money in exchange for shares in the ETF. The shares are then traded like shares of any other company.

Investors are allowed to give up their shares in exchange for the underlying assets. Investors can also obtain additional shares by adding assets with the same components as those already in the ETF.

Mutual funds and ETFs are significantly regulated in most jurisdictions to ensure that complete and accurate financial information is given to prospective investors. Despite the regulation, some undesirable trading behavior in mutual funds include:

• Late trading: This involves using market developments that occur after 4 pm to cancel or to carry out trade. An offense that is punishable by the law.
• Market timing: Market timing is brought about by the existence of stale prices (prices that do not reflect recent information or those that differ due to time zone differences). Market timing is not illegal; however, it requires large funds for it to be worthwhile.
• Front running/Tailgating: This is where traders use acquired information to trade for themselves before trading for their firm/clients. Front running is illegal in fund management.
• Directed brokerage: This Involves a contract between a mutual fund and a brokerage house. The mutual fund agrees to carry its trades through the brokerage house, which agrees to recommend the fund to its clients. It is legal but frowned upon by regulators.

## Hedge Funds

Hedge funds are alternative investments that utilize pooled funds and use different investment strategies to earn active returns. For instance, hedge funds use derivatives and leverage to create high returns.

Hedge funds have fewer regulations than mutual funds, can follow a diverse approach of trading strategies, and are not required to disclose their holdings on a daily basis. They, however, have additional restrictions on how to solicit funds from investors.

Other differences between mutual and hedge funds are stated below:

$$\begin{array}{l|l|l} \textbf{Basis for Comparison} & \textbf{Mutual Funds} & \textbf{Hedge Funds} \\ \hline \text{Flexibility} & \text{The manager has lots of constraints} & \text{The manager has fewer constraints.} \\ {} & \text{to deal with, e.g., limited use of} & \text{Can use leverage, sell short, or} \\ {} & \text{leverage.} & \text{even use derivatives.} \\ \hline \text{Paperwork} & \text{Offered via a prospectus.} & \text{Offered via a private placement} \\ {} & {} & \text{memorandum.} \\ \hline \text{Liquidity} & \text{Investors can withdraw their} & \text{Investors can only get their} \\ {} & \text{money any day.} & \text{money periodically.} \\ \hline \text{Self-investment} & \text{The manager does not have to put} & \text{As a sign of good faith, the} \\ {} & \text{some of their capital in the fund.} & \text{manager is expected to put} \\ {} & {} & \text{some of their money in the fund.} \\ \hline \text{Advertisement} & \text{May advertise freely.} & \text{Not free to advertise in the} \\ {} & {} & \text{public.} \\ \hline \text{Listing} & \text{Maybe listed, i.e., closed-end} & \text{Cannot be listed on an exchange.} \\ {} & \text{funds.} & {} \\ \end{array}$$

## Hedge Fund Fees, Hurdle Rate, High-Water Mark Clause, and Clawback

Compared to mutual funds, hedge funds charge investors higher management/operational fees. These include:

• An annual management fee of 1%-3% of assets
• An incentive fee of 15%-30% of realized net profits

A typical hedge schedule that reads “2% plus 30%,” for example, indicates that the fund charges 2% per year of assets under management and 30% of net profit. These high charges are designed to attract the best hedge managers.

The management fee is computed on the assets at the beginning of the year, and the incentive fee is calculated after subtracting the management fee.

The incentive is equivalent to a call option on the net profit generated by the funds for an investor in a given year. For instance, consider the “2% plus 30%” fee structure of a fund. Then the incentive fee is calculated as:

$$\text{Incentive Fee} = 0.3 \times \text{max}\left(R\times A-0.02\times A,0\right)$$

Where

A = assets under management at the beginning of the year.

R = return on the assets during the year.

Note that the strike price of the above analogous call option is 2% of the assets under management.

Example: Calculating the Incentive Fee, Management Fee, and Return on a Hedge Fund

Century Capital is a hedge fund with a 100 million initial investment. The fund charges a 2% management fee based on the beginning of year assets under management and a 20% incentive fee. In its first year, the capital earns a 25% return. What are the management fee, incentive fee, and return on the capital? Solution \begin{align}\text{Management Fee} &= 2\% \times 100 =\ 2 \text{milion}\\\text{Incentive fee} &= 0.2\times \text{max}\left(R\times A-0.02\times A,0\right)= 0.2\times \text{max}\left(25-2,0\right) = \4.60 \text{ million}\\ \text{Total fee} &= \ 2 \text{ milion}+\4.60 \text{ million}=\6 \text{ million}\\ \text{Return on the hedge fund}&=\frac{\ 125 \text{ milion}-\ 100 \text{ milion}-\ 6.60 \text{ milion}}{\ 100 \text{ milion}} -1=18.40\%\end{align} As a precondition for imposing high incentive fees, investors may be offered several guarantees. These include: • Hurdle rate: This is the minimum return that should be earned before the incentive fees are imposed. • High-water mark clause: This requires the fund to recoup any prior losses before the investment manager is allowed to impose an incentive fee. Prior losses may be comprised of performance losses, management fees, and administrative fees. A proportional adjustment clause may apply so that if the investor suffers a loss and simultaneously withdraws part of their capital, the amount of previous loss to be recouped is adjusted proportionally. • Clawback: A clawback is an action where hedge investors take back the incentive fees previously awarded to the hedge fund manager so as to offset current losses. A portion of the incentive fees is held in a recovery account so that when the investor makes a loss, they receive some compensation from that account. Example: Calculating the Return on a Hedge Fund Investment with a Hurdle Rate Century Capital is a hedge fund with a100 million initial investment. The fund charges a 2% management fee based on the beginning of year assets under management and a 20% incentive fee. Moreover, the fee structure specifies a hurdle rate of 4%, and the incentive fee is based on the excess of the hurdle rate.

In its first year, the capital earns a 25% return. What are the management fee, incentive fee, and return on the hedge fund investment?

Solution

\begin{align}\text{Management Fee} &= 2\% \times 100 =\ 2 \text{ milion}\\ \text{Incentive fee} &= 0.2\times[125-100-5-2,0]= \3.60 \text{ million}\\ \text{Total fee} &= \ 2 \text{ milion}+\3.60 \text{ million}=\5.60 \text{ million}\\ \text{Return on the hedge fund investment}&=\frac{\ 125 \text{ milion}-\ 100 \text{ milion}-\ 5.60 \text{ milion}}{\ 100 \text{ milion}} -1=19.40\%\end{align}

## Prime Brokers

A prime broker handles the transactions of a hedge fund. These transactions include: lending them money, providing risk management services, providing hedging services, and carrying out stress tests on their portfolio. Common prime brokers are banks.

## Common Hedge Fund Strategies

1. #### Long/Short Equity:

As the name suggests, the long/short equity strategy involves maintaining long and short positions in equity and equity derivative securities. The fund manager buys the stocks they feel are undervalued while simultaneously selling those they feel are overvalued. Usually, the value of shares shorted is equal to the shares bought, and the sensitivity of both long and short positions should be the same as that of the market.

2. #### Dedicated Short :

The aim of dedicated short is to earn a return by maintaining a net short position in the market through a combination of long and short positions. This means that short positions take the lion’s share of the fund’s overall positions. In other words, a dedicated short fund focuses on identifying overvalued stocks.

3. #### Distressed Securities:

A distressed debt strategy is an event-driven strategy that tends to focus on companies in distress (financial trouble). Positions in bonds or stocks can be both long and short. Funds that employ this strategy imposes more stringent lock-up and withdrawal terms.

4. #### Fixed-Income Arbitrage:

Fixed income strategy seeks to profit from discrepancies in related fixed income instruments. The manager might buy-long a bond that they feel is undervalued and simultaneously sell-short a similar bond they think is overvalued.

5. #### Convertible Arbitrage:

Convertible arbitrage strategy seeks to profit from discrepancies in a company’s convertible securities relative to its stock. It might involve taking a long position in a company’s convertible securities and simultaneously taking a short position in its stock.

6. #### Merger Arbitrage:

Merger arbitrage strategy entails taking opposing positions in two firms that are about to merge. The goal is to exploit price inefficiencies that may occur before and after a merger. In most cases, a merger announcement is followed by a spike in the stock of the acquiring company and a dip in the stock of the target. The latter is especially associated with failed bids. For a cash bid, the price paid for each stock is usually at a premium to the market price. Offers can take the form of cash or stock of the bidding firm. For a cash bid, the risk arbitrage position consists of buying the target’s stock and then waiting for it to move to the takeover price. For a stock exchange deal, the acquirer offers to exchange each target share for Δ shares of the acquirer. The arbitrage position, therefore, consists of a long position in the target offset by a short position of Δ in the acquirer’s stock.

7. #### Emerging Markets:

The emerging-market strategy involves debt/equity investing in emerging markets. It’s a strategy that aims to identify emerging market shares that are overvalued or undervalued.

8. #### Global Macro:

Global macro strategy is a general investment strategy that involves making investment decisions guided by the economic/political outlook of a country. In other words, the strategy reflects global macroeconomic trends. They look for countries where the market seems not to be in equilibrium and place bets that the market will adjust and attain equilibrium once again.

9. #### Managed Futures:

The manager invests in financial and commodities futures markets. They make directional bets with long/short positions.

## Research on Returns

### Mutual Fund Research

Actively managed mutual funds have been unable to beat the market after expenses for the past decades. This has been attributed to the fact that the market return is the return to all investors before expenses.

Through a test called the persistence test, it has also been established that only half of the mutual funds could outperform a market in subsequent years after beating the market in the previous year. These findings have made investors prefer index funds to actively managed funds because index funds charge a lower fee and perform better.

Hedge Fund Research

Some hedge funds have been seen to report a good performance for a few years and then lose a large percentage of the funds under management.

The Barclay Hedge offers an index tracking of all hedge funds. Generally, Hedge funds perform better in bear markets and underperform in bull markets.

### Risks Faced by Hedge Funds

• Liquidity risk: occurs when the fund invests in illiquid assets Liquidity is a function of (I) the size of the position and (II) intrinsic liquidity of the instrument.
• Pricing risk: some of the assets can be quite difficult to price, e.g., derivatives
• Counterparty risk: The manager gets into contracts with dealers, brokers, and clearing agents. There’s always a risk that these parties will renege on their obligations, putting the fund on the path of unprecedented losses.
• Short squeeze risk: The fund manager may be forced to purchase security they had sold short sooner than anticipated when the investor from whom the security was borrowed comes calling early.
• Settlement risk: One or more parties in a transaction may fail to deliver securities as per the contract.

## Hedge Fund Performance

There are no reliable data records that can help us to assess hedge fund performance over the years. Part of that has much to do with the discretion with which some hedge funds are managed. Studies have shown that most investors in hedge funds are drawn to the industry largely because of several biases. These include:

• Hedge funds tend to have a higher net return than bonds and stocks.
• Hedge funds exhibit lower volatility of returns compared to equities.
• Hedge fund Sharpe ratios tend to be higher than those of equities and bonds.

### Question 1

Longeren Mutual fund had year-end assets of $40 million and liabilities amounting to$10 million. If the total number of outstanding shares is 1,0000,000, what is the fund’s net asset value?

1. 30
2. 40
3. 50
4. 20

Solution

\begin{align*} \text{NAV}&=\frac{\text{Market value of assets at the close of the day}- \text{Liabilities}}{\text{Number of outstanding shares}} \\&=\frac{40,000,000-10,000,000}{1,000,000}\\&=30\end{align*}

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