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Hedge funds that do not use leverage will not generate much interest expense
7.2 The process of converting gains to a standard holding period tends to amplify returns, which can be misleading especially when very short time periods are annualized. Also, when comparing nominal returns of many hedge funds over a fixed period of time (a quarter, for example), nominal returns can be fairly compared with no further adjustment.
7.3 The investor has a different investment each time the value of assets change and interest accrues. By not liquidating an investment at the interim value, the investor is implicitly reinvesting. The average of the beginning and ending values approximates a more complete average that includes daily values throughout the period. In using an average, the return acknowledges that the investor should expect a return on the intraperiod returns.
7.4 The compound return incorporates return on return that occurs during the year. This return on return (or interest on interest) is more valuable if the return is received more frequently and is more valuable for higher rates of return.
.5 The convention goes back to a time before computers were common. Interest was retrieved from tables of interest accruals. To simplify calculations, all months were deemed to have 30 days and all years had 360 days. The tables were much more compact than tables that would be required if actual days were used in the calculations.
7.6 Rates are quoted with knowledge of the day-counting convention. For example, the effective rate of a simple interest quoted on the basis of a 360-day year is about 1.5 percent higher than the stated rate (5 days/360 days). Rates are quoted so that the effective rates are consistent with market levels.
7.7 When payments are made or received at different times, the investor is not indifferent about the timing of the payments. It is better to receive payments early, so that the funds can be invested and earn interest. In calculating present value, delayed payments are adjusted to a level equivalent to an immediate payment, at least with respect to the interest that could have been earned between the present time and the time of the delayed payment.
7.8 The future value represents the amount of a cash flow in the future that is economically equivalent to a cash flow (or multiple cash flows) that occurs earlier. The early cash flows are adjusted as if they were invested at prevailing interest rates and the interest that could be earned is added to the cash flows.
7.9 If a positive return is followed by a loss of the same percentage, the average of these two rates will be zero, but the portfolio will be worth less than the starting value. For example, if a 10 percent loss follows a 10 percent gain, the value of $1 invested in the fund prior to these two periods would be $1 (1 + 10%) (1 - 10%) = $.99. The geometric return captures this phenomenon might be necessary to use 366 days for the days in the year depending on the kind of asset the return applies to). Therefore, the annual return is 10% 365/31 = 117.74%.
Another major day-counting protocol is the 30/360 day count, whereby each month is assumed to contain 30 days and each year has 360 days. This protocol is not typically used for hedge fund returns, but the calculation would be: 10% 360 /30 = 120%.
7.13 One dollar invested in the first investment will return $1.10 a year later. A dollar invested at 9.65 percent compounded monthly will pay 9.65%/12 after one month; then apply the same interest rate factor to the principal and interest the next month. The reinvestment continues through the year. At the end of the year, the second dollar would grow to (1+9.65%/12)12 or $1.1009. Although this is fairly close to the annual investment at 10 percent, the return is somewhat higher on the second alternative (i.e., 1.1009 1.10). The investment paying 9.65 percent has a higher effective return. If the second investment paid 9.57 percent, the two alternatives would offer identical returns after a year because (1 + 9.57%/12)12 = 1.10.
The second investment assumes that the interim interest also accrues at exactly 9.65 percent. From the wording of the question, it is clear that the investment will accrue the interest monthly and will compound at the 9.65 percent rate, to be paid at the end. If the second investment made actual payments each month, it is important to realize that the return indicated would only occur if the payments are reinvested at the same rate as the initial investment.
7.19 The standard deviation of return (also called volatility) is 4.36 percent or 15.09 percent annualized. In this case, the standard deviation was annualized with the scaling factor sqrt(12) to transform from monthly to annual. The standard deviation is usually calculated from continuously compounded returns. Since question 7.18 did not specify the compounding frequency, the data were used as given. It is, of course, fairly likely that such data are nominal returns (implicitly com
pounded monthly). Had the rates been converted from monthly compounding to continuous, the standard deviation would have been 14.81 percent.
7.20 The 1.64 percent monthly rate is equivalent to an annual rate of 20.56 percent semiannually compounded. Both rates result in a future value of $1.216 one year in the future.
7.21 The 1.64 percent monthly rate is equivalent to an annual rate of 19.57 percent continuously compounded. Both rates result in a future value of $1.216 one year in the future.
The deviations are calculated as the difference between the threshold (zero) and the monthly return, although positive differences are treated as a deviation of zero. The deviations are squared and summed. The monthly downside semivariance is the sum divided by 11 (12 months less 1). The annualized downside semivariance is 12 times the monthly semivariance. The downside deviation is the square root of the downside semivariance.
7.23 The Sharpe ratio and Sortino ratio can be calculated from the monthly data or annualized values. The arithmetic average is used in the numerator because the arithmetic average is used in the standard deviation calculation as an investment adviser would increase the reporting requirements and might create problems in collecting incentive fees, unless all the investors are accredited investors, anyway. However, it is possible to register hedge funds, and this is a growing trend. Most commonly, funds of funds register but are permitted to invest in unregistered hedge funds. Although this registration doesnt simplify anything for the individual hedge funds, it has allowed funds of funds to offer their funds to investors with sharply lower minimum investments.
.2 A Section 3(c)(1) hedge fund is permitted to have not more than 100
investors, so this fund may admit one more investor as a partner. Employees and other key insiders do not count toward the limit, so the hedge fund could admit the trader and an additional outside investor without violating the limitation under Section 3(c)(1). Funds subject to a limitation on investors may begin restricting access to the fund before reaching the limit. A fund that has even 95 investors might turn down smaller investments so that it has capacity to accept larger investors. This fund might consider converting to a Section 3(c)(7) fund. This would mean that certain investors who qualify as accredited investors but not as qualified purchasers would be barred from investing in the fund. However, the hedge fund could allow the existing investors to remain in the fund even after adopting the Section 3(c)(7) exemption even if they are not qualified purchasers.
8.3 Yes. In any case, the hedge fund is permitted to admit up to 35 investors who are not accredited, although admitting nonaccredited investors increases the reporting requirement on the fund. However, employees who are partners need not be accredited.
8.4 A person may be a qualified purchaser based on his or her net worth. Investors who do not have enough income or wealth may still be qualified purchasers. An investor with sufficient assets or income but inadequate investment sophistication would still be a qualified purchaser. However, the investor could argue that the hedge fund was an inappropriate investment for someone of his investment experience.
This type of lawsuit is very fact specific and the success of this suit would depend on a variety of facts not known from the question. In particular, the investor likely signed a document asserting that he had sufficient experience and knowledge to make the decision to invest in this fund. The investor has the resources to have hired accountants, lawyers, tax experts, and investment advisers to review the investment before becoming an investor. If the investor consulted any such experts, it might affect his claim for restitution. Finally, although the hedge fund lost money (presumably 100 percent of its capital), the losses dont automatically mean that the investment would have been considered a risky investment at the time the investor became a partner.
On the other hand, the possibility of such a suit demonstrates why a hedge fund manager should review the background of each investor. In the event of losses, it is very likely that a fund and its managers will be sued for restitution by at least some investors.
.5 Offshore hedge funds are not subject to the investor limit imposed by Section 3(c)(1) and Section 3(c)(7) because the funds are not governed by U.S. securities laws. These funds are already exempt.
8.6 One easy way to get more investors is to have them invest indirectly through a fund of funds. Generally, a fund that accepts an investment from a fund of funds counts this as one investment and does not need to count the individual fund of funds investors. The fund would need to include the investors in its own total if the fund existed just to consolidate investors. Similarly, a fund that cloned itself would also need to add up the investors in nearly identical funds.
The integration rules and look-through provisions are very complicated. The rules were intended to prevent hedge funds from structuring gimmicks to get around the investor limitations. In fact, Section 3 (c)(7) funds that are organized as master-feeder funds generally have enough flexibility to have no capacity problems.
8.7 Tax-exempt investors may have trouble with hedge funds that have substantial interest expenses. Hedge funds that borrow money to carry long positions generate interest expenses. The higher the leverage, the more interest expense is generated.
Hedge funds that do not use leverage will not generate much interest expense. Hedge funds that use leverage may be able to reduce their interest expenses by relying on derivative instruments instead of cash securities and borrowed money.
Hedge funds that borrow securities may receive interest income on collateral. This interest income probably will not lead to tax problems for a taxexempt investor.
Hedge funds organized within the United States usually do not incorporate. Instead, these funds set up as partnerships or limited liability corporations taxed as partnerships. Because the domestic funds flow through income and expense items, they avoid being taxed as businesses. Instead, the individual income and expense items flow through to investors. Tax-exempt investors can invest in offshore hedge funds, which do not pass through interest expenses because the corporation does not flow through the income and expenses. Instead, the corporation reports the income and pays tax (if any) on the net income. Tax-exempt investors are not allocated interest expenses.
8.8 The law aims to prevent hedge funds from accepting money from terrorist groups and organized crime. This source of funds probably does not constitute a large amount of assets, so this direct impact will be small.
The considerably larger burden placed on hedge funds is the cost of ensuring compliance. Hedge funds now have a duty to know much more about their customers. A small portion of hedge fund investors may value their privacy so highly that they may elect to invest in hedge funds that are not covered by the Act. Certainly hedge funds operated within the United States must comply regarding both their domestic and their offshore customers. Offshore hedge funds may need to comply as well if they accept money from U.S. residents or conduct business within the United States.
Part of the problem complying is that there is not yet a clear understanding of what constitutes proper compliance. Hedge fund managers could be held to be in violation if the courts require greater effort than is currently being made. Hedge funds risk being held retroactively to a standard once the courts define what constitutes adequate effort to know about their customers.
8.9 Antifraud rules and regulations govern all investment managers, regardless of how or whether a hedge fund is registered.
8.10 One reason why a hedge fund may prefer to avoid registration is to avoid making some of the disclosures required of a public company. For this reason, investors often receive less information about hedge fund investments than they would receive about mutual fund positions or other registered investment portfolios.
Investors may demand more disclosures than the minimum required of an unregistered hedge fund. The investor may receive as much information as would be disclosed if the investment was registered. Hedge funds do not need to make uniform disclosures to all investors, so some investors may be able to demand transparency and daily net asset values and other investors may receive only highly aggregated disclosures and no interim valuations particular positions, it does provide enough information to calculate the leverage. Suppose the hedge fund had $3 in debt and $1 in equity. The fund would have $4 in assets. To calculate leverage, divide the assets by the hedge fund capital. This hedge fund is levered 4:1. The general case is:
A = Total assets held by the hedge fund D = Total liabilities of the hedge fund
E = Equity or partners capital A = D + E
This is true for any capital structure!
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