Which of the following would increase the net asset value of a mutual fund share assuming all other things remain unchanged?

13.7.1 Net Asset Value (NAV)

A REIT’s NAV is the estimated market value of its properties and other assets less the amount of short- and long-term liabilities, as well as the book value of any preferred stock outstanding. This value is typically stated on a per-share basis by taking the total NAV and dividing it by the common stock equivalents.

NAV per share is often compared to the current stock price. If NAV per share is greater than the stock price, the REIT is said to be trading “at a premium to NAV.” If NAV is below the share price, it trades “at a discount” to NAV. A stock trading at a discount to NAV implies that if liquidated, the company’s assets could be sold, its liabilities and preferred stock repaid, and the balance available for distribution would exceed its current stock price.

NAVpershare=(market valueofassets−liabilities−preferredstock)/commonshareequivalents

NAV also relates to another metric: implied cap rate. To determine the implied cap rate, divide the REIT’s NOI by its total market capitalization.

Impliedcap rate=(NOI/totalmarketcapitalization)

The REIT’s NAV equals the sum of the values of all of the REIT’s assets. In the NAV calculation, the value of each asset is calculated using actual NOI multiplied by an estimate of the market cap rate. If the REIT’s actual stock price equals its NAV per share, the weighted average market cap rate and the implied cap rate will be the same and the REIT stock is trading at its liquidation value.

12.1.2 Overall Return as the Weighted Sum of Individual Returns

The linking of individual segment returns to obtain an overall portfolio return is fundamental for attribution analysis. In the following a formula will be derived, by which the overall return of a portfolio can be derived by means of the initial weights of the securities.

At first, for the sake of simplicity we will look at the special case, where the portfolio consists of two segments. The return of the two segments (e.g. equity and bond segment) in the interval from 0 to T will be denominated by srp1 and srp2 , respectively (see Table 12.1).

Table 12.1. Notation for the Net Asset Value of the Portfolio Segments

The notation for the net asset values (or Inventory) of the segments is given in the following table. If the weights of the segments at the beginning of the period are denoted by swp1 and swp2 then the following holds: (see Figure 12.1.)

swp1=I10I10+I20,respectively swp2=I20I10+I20.

At this stage it is assumed that no exogenous cash-flows occur in each of the segments. Under this assumption the returns srp1 and srp2 are given by:

srp1=I1T-I10I10,respectivelysrp2=I2 T-I20I20.

The return RP of the overall portfolio is given by:

RP=I1T+I2T- I10-I20I10 +I20.

In order to derive the desired formula for the overall return of a portfolio with two segments, the expression on the right-hand side of this equation will be modified as follows:

RP=I1T-I10 I10+I20+I 2T-I20I10+I20=I10I10+I20∗I1T-I10I10+I20I10+I20∗I2T-I20I20=swp1∗srp1+swp2∗srp2.

Under the assumption that no exogenous cash flows have occurred, the overall return of a portfolio broken down in several segments is thus identical to the weighted sum of the individual segment returns. In particular:

Segment contribution = initial weight of the segment * segment return.

In the following we make the assumption that the weights of the segments at the beginning of the period are based on the closing prices of the assets of the previous trade day. The calculation of the return contributions over the period from 01.07.2007 to 31.07.2007 is for instance based on the weightings derived from closing prices as at 30.06.2007 (cf. the following example).

These considerations can easily be generalized to a return decomposition for a portfolio with an arbitrary number of segments.

Representation of the overall return as the sum of return contributions

The return RP of a portfolio consisting of n segments over a period, in which no exogenous cash-flows have occurred, is given by the weighted sum of the segment returns.

(12.1)RP= swp1∗srp1+swp2∗srp 2+⋯+swpn∗srpn=∑i=1nswpi∗srpi,

where:

srpi: return of the portfolio segment i over the period

swpi: weighting of the portfolio segment i at the beginning of the period ∑i=1nswpi=1.

The terms swpi∗srp i are called return contributions of the portfolio segments.

The return contributions of the individual benchmark components are computed analogous to those of the portfolio, such that the return RB of the benchmark over a period, in which no adjustment of the weights has occurred (cf. Equation (12.1)), is given by:

(12.2)RB=swb1∗srb1+swb2∗srb2+⋯+swbn∗srbn=∑i=1nswbi∗srb i,

where:

srbi: return of the benchmark segment i over the period

swbi: weighting of the benchmark segment i at the beginning of the period ∑ i=1nswbi=1

n: number of segments within the benchmark and the portfolio.7

The terms swbi∗srbi are called return contributions of the benchmark segments.

The goal of an attribution analysis relative to a benchmark is to find out, how the different weightings of the segments have contributed toward the active return

(12.3)RP-RB=∑i=1nswpi∗srpi-swbi∗srbi.

The terms on the right-hand side

(12.4)swpi∗srpi-swbi∗srbi

represent the differences of the return contributions of the individual segments.

In the following we will consider the special case, in which all segments consist of a single stock. In this case the returns srbi and srpi are identical, so that Equation (12.3) can be written in a simplified form:

(12.5)RP-RB=∑i=1n (swpi-swbi)∗srbi.

In regard to the sign of (swpi-swbi) ∗srbi four different cases need to be distinguished.

The return contribution of (swpi-swbi)∗srbi is positive, if the portfolio was overweight in the stock i and the stock had a positive return, or if the portfolio was underweight and the stock had a negative return. It is negative, if the portfolio was overweight in case of a negative stock return, or if the portfolio was underweight in case of a positive stock return.

There is, however, a problem with this equation. An overweight sector with a positive benchmark return will give a positive contribution even if the stock underperforms the benchmark. This will be avoided if one uses in Equation (12.5) the active returns relative to the benchmark, srbi-RB, instead of the absolute returns srbi. Then the return contributions will have the following form:

(12.6)(swpi-swbi)∗(srbi-RB).

Also the modified return contributions in (12.6) sum up to the active return RP-RB. According to Equation (12.5) it holds that:

RP-RB=∑i=1n(swpi-swbi)∗srbi .

Using this identity we obtain:

∑i=1nswpi-swbi∗srb i-RB=∑i=1n swpi-swbi∗srbi -∑i=1nswpi- swbi∗RB=RP-RB-(1-1)∗RB=RP-RB,

according to the claim.

To conclude both approaches for a relative attribution methodologies are summarized.

Return contributions of individual stocks to the active return

The relative return contributions of the single stocks toward the active return of a portfolio relative to its benchmark (in a period without exogenous cash-flows) can be calculated in two different ways:

The (absolute) return of a stock is multiplied by the initial active weight as at the beginning of the period:

(12.7)(swpi-swbi)∗srbi.

The return of a stock relative to a benchmark is multiplied by the initial active weight as at the beginning of the period:

(12.8)(swpi -swbi)∗(srbi-RB) ,

where:

RB : benchmark return over the period

srbi : return of the stock i over the period

swbi : weighting of the stock i in the benchmark at the beginning of the period ∑ i=1nswbi=1

swp i : weighting of the stock i in the portfolio at the beginning of the period ∑i=1n swpi=1

n : number of stocks in the benchmark and the portfolio.

In both cases the relative contributions add up to the active return.

Balance-Sheet Considerations

For financial-reporting purposes, the purchase price (PP) paid, including the fair value of any noncontrolling interest (FMVNCI) in the target at the acquisition date, for the target company consists of the FMV of total identifiable acquired tangible and intangible assets (FMVTA) less total assumed liabilities (FMVTL) plus goodwill (FMVGW). The difference between FMVTA and FMVTL is called net asset value. The purchase price is the total consideration transferred to target firm shareholders for net acquired assets less any interest not owned by the acquirer (i.e., noncontrolling interest). These relationships can be summarized as follows:

(12.1)Purchase price (total consideration):PP=FMVTA−FMVTL+FMVGW−FMVNCI

(12.2)Goodwill:FMVGW=PP+FMVNCI−FMVTA+FMVTL=( PP+FMVNCI)−(FMVTA−FMVTL)

From Eq. (12.2), as net asset value increases, FMVGW decreases, for a given purchase price. Therefore, goodwill can be either positive (i.e., PP > net asset value) or negative (i.e., PP < net asset value). Negative goodwill arises if the acquired assets are purchased at a discount to their FMV and is referred to under SFAS 141R as a “bargain purchase.”41

Table 12.5 shows how acquisition accounting can be applied in business combinations. Assume Acquirer buys 100% of Target’s equity for $1 billion in cash at yearend. Columns 1 and 2 present the preacquisition book values on the two firms’ balance sheets. Column 3 reflects the restatement of the book value of the Target’s balance sheet in column 2 to their FMV. As the sum of columns 1 and 3, column 4 presents the Acquirer’s postacquisition balance sheet. This includes the Acquirer’s book value of the preacquisition balance sheet plus the FMV of the Target’s balance sheet. In column 3, total assets are less than shareholders’ equity plus total liabilities by $100 million, reflecting the unallocated portion of the purchase price, or goodwill. This $100 million is shown in column 4 as goodwill on the postacquisition Acquirer balance sheet to equate total assets with equity plus total liabilities. Note that the difference between the Acquirer’s pre- and postacquisition equity is equal to the $1 billion purchase price.

Table 12.5. Example of Acquisition Method of Accounting

Exhibit 12.1 shows the calculation of goodwill in a transaction in which the acquirer purchases < 100% of the target’s outstanding shares but is still required to account for all of the target’s net acquired assets, including 100% of goodwill. Exhibit 12.2 lists valuation guidelines for each major balance-sheet category.

Exhibit 12.1

Estimating Goodwill

On the closing date, Acquirer Inc. purchased 80% of Target Inc.’s 1 million shares outstanding at $50 per share, for a total value of $40 million (i.e., 0.8 × 1000,000 shares outstanding × $50/share). On that date, the fair value of the net assets acquired from Target was estimated to be $42 million. Acquirer paid a 20% control premium, which was already included in the $50-per-share purchase price. The implied minority discount of the noncontrolling (minority) shares is 16.7% [i.e., 1 − (1/(1 + 0.2)].a What is the value of the goodwill shown on Acquirer’s consolidated balance sheet? What portion of that goodwill is attributable to the noncontrolling interest retained by Target’s shareholders? What is the FMV of the 20% noncontrolling interest per share reflecting the minority discount?

Goodwill shown on Acquirer’s balance sheet: From Eq. (12.2), goodwill (FMVGW) can be estimated as follows:

FMVGW=(PP+FMVNCI) -(FMVTA-FMVTL)=($40,000,000+$10,000,000)-$42,000,000=$8,000,000

Goodwill attributable to the noncontrolling interest: Note that 20% of the total shares outstanding equals 200,000 shares, with a market value of $10 million ($50/share × 200,000). Therefore, the amount of goodwill attributable to the noncontrolling interest is calculated as follows:

Fair value of the noncontrolling interest per share: Since the fair value of Acquirer’s interest in Target and Target’s retained interest are proportional to their respective ownership interest, the value of the ownership distribution of the controlling (majority) and noncontrolling (minority) owners is as follows:

The FMV per share of the noncontrolling interest is $41.65 [i.e., ($10,000,000/200,000) × (1 − 0.167)]. The noncontrolling interest share value is less than the share price of the controlling shareholders (i.e., $50/share) because it must be discounted for the relative lack of influence of noncontrolling or minority shareholders on the firm’s decision-making process.

Exhibit 12.2

Guidelines for Valuing Acquired Assets and Liabilities

Cash and accounts receivable, reduced for bad debt and returns, are valued at their values on the books of the target on the acquisition/closing date.

Marketable securities are valued at their realizable value after transaction costs.

Inventories are broken down into finished goods and raw materials. Finished goods are valued at their liquidation value; raw material inventories are valued at their current replacement cost. Target last-in, first-out inventory reserves are eliminated.

Property, plant, and equipment are valued at the FMV on the acquisition/closing date.

Accounts payable and accrued expenses are valued at the levels stated on the target’s books on the acquisition/closing date.

Notes payable and long-term debt are valued at their net present value of the future cash payments discounted at the current market rate of interest for similar securities.

Pension fund obligations are booked at the excess or deficiency of the present value of the projected benefit obligations over the present value of pension fund assets. This may result in an asset’s or liability’s being recorded by the consolidated firms.

All other liabilities are recorded at their net present value of future cash payments.

Intangible assets are booked at their appraised values on the acquisition/closing date.

Goodwill is the difference between the purchase price and the FMV of the target’s net asset value. Positive goodwill is recorded as an asset, whereas negative goodwill (i.e., a bargain purchase) is shown as a gain on the acquirer’s consolidated income statement.

Table 12.6 illustrates the balance-sheet impacts of acquisition accounting on the acquirer’s balance sheet and the effects of impairment subsequent to closing. Assume that Acquirer Inc. purchases Target Inc. on December 31, 2019 (the acquisition/closing date), for $500 million. Identifiable acquired assets and assumed liabilities are shown at their fair value on the acquisition date. The excess of the purchase price over the fair value of net acquired assets is shown as goodwill. The fair value of the “reporting unit” (i.e., Target Inc.) is determined annually to ensure that its fair value exceeds its carrying (book) value. As of December 31, 2020, it is determined that the fair value of Target Inc. has fallen below its carrying value, due largely to the loss of a number of key customers.

Table 12.6. Balance-Sheet Impacts of Acquisition Accounting

In January 2017, the Financial Accounting Standards Board issued revised guidance for goodwill impairment testing to make the process simpler and less expensive. The new guidance found in Accounting Standards Update No. 2017-04 replaces the current two-step process for testing goodwill for a decrease in value with a one-step procedure.

The process for valuing goodwill impairment under GAAP involves the following steps:

Calculate the fair value of the business and compare it to the carrying or book value of the business. If the carrying value exceeds fair value, perform the next step. Otherwise, the testing stops.42

Estimate the fair value of the identifiable assets and liabilities that support the goodwill and compare to their carrying values on the firm’s balance sheet to determine a new estimate of goodwill. If the new estimate of goodwill is less than the carrying value of goodwill on the firm’s balance sheet, the carrying value must be reduced by the difference and shown as a pretax loss on the firm’s income statement.

The new standard removes Step 2 of the goodwill impairment test, which requires a hypothetical acquisition purchase price allocation. Goodwill impairment will now be the amount by which a business unit’s carrying value exceeds its fair value, not to exceed the carrying amount of goodwill. Public companies that file reports with the SEC must adopt the new standard for fiscal years beginning after December 15, 2019. Those that are not SEC filers have until December 15, 2020.

The treatment of impaired goodwill according to international accounting standards is different from GAAP. International standards take into account that some portion of an asset may be recoverable if sold and that the asset may still have some value if used in some portion of the firm’s operations. Therefore, the recoverable amount of an asset is either the asset’s fair value less costs to sell or its value in use, whichever is greater. To measure impairment, the assets carrying amount is compared to its recoverable amount, which is the amount determined for individual assets. The impairment loss is allocated by reducing any goodwill of the business unit and then reducing the carrying value of other assets of the business unit on a pro rata basis.

Balance-Sheet Considerations

For financial-reporting purposes, the purchase price paid, including the fair value of any noncontrolling interest (FMVNCI) in the target at the acquisition date, for the target company consists of the FMV of total identifiable acquired tangible and intangible assets (FMVTA) less total assumed liabilities (FMVTL) plus goodwill (FMVGW). The difference between FMVTA and FMVTL is called net asset value. PP is the total consideration transferred to target firm shareholders for net acquired assets less any interest not owned by the acquirer (i.e., noncontrolling interest). These relationships can be summarized as follows:

(12.1)Purchase price(totalconsideration):PP= FMVTA−FMVTL+FMVGW−FMV NCI

(12.2)Goodwill:FMVGW=PP+FMVNCI −FMVTA+FMVTL=(PP+FMVNCI)−(FMVTA−FMVTL)

From Eq. (12.2), it should be noted that as net asset value increases, FMVGW decreases. Also note that the calculation of goodwill can result in either a positive (i.e., PP > net asset value) or a negative (i.e., PP < net asset value). Negative goodwill arises if the acquired assets are purchased at a discount to their FMV and is referred to under SFAS 141R as a “bargain purchase.”31

Table 12.4 illustrates how the purchase method of accounting can be applied in business combinations. Assume Acquirer buys 100% of Target’s equity for $1 billion in cash on December 31, 2014. Columns 1 and 2 present the preacquisition book values of the two firms’ balance sheets. Column 3 reflects the restatement of the book value of the Target’s balance sheet in column 2 to their FMV. As the sum of columns 1 and 3, column 4 presents the Acquirer’s postacquisition balance sheet. This includes the Acquirer’s book value of the preacquisition balance sheet plus the FMV of the Target’s balance sheet. As shown in column 3, total assets are less than shareholders’ equity plus total liabilities by $100 million, reflecting the unallocated portion of the purchase price, or goodwill. This $100 million is shown in column 4 as goodwill on the postacquisition Acquirer balance sheet to equate total assets with equity plus total liabilities. Note that the difference between the Acquirer’s preacquisition and postacquisition equity is equal to the $1 billion purchase price.

Table 12.4. Example of Purchase Method of Accounting

FMV, Fair market value.

Exhibit 12.1 shows the calculation of goodwill in a transaction in which the acquirer purchases less than 100% of the target’s outstanding shares but is still required to account for all of the target’s net acquired assets, including 100% of goodwill. Exhibit 12.2 lists valuation guidelines for each major balance-sheet category.

Exhibit 12.1

Estimating goodwill

On January 1, 2014, the closing date, Acquirer Inc. purchased 80% of Target Inc.’s 1 million shares outstanding at $50 per share, for a total value of $40 million (i.e., 0.8 × 1,000,000 shares outstanding × $50/share). On that date, the fair value of the net assets acquired from Target was estimated to be $42 million. Acquirer paid a 20% control premium, which was already included in the $50-per-share purchase price. The implied minority discount of the noncontrolling (minority) shares is 16.7% [i.e., 1 − (1/(1 + 0.2)].a What is the value of the goodwill shown on Acquirer’s consolidated balance sheet? What portion of that goodwill is attributable to the noncontrolling interest retained by Target’s shareholders? What is the FMV of the 20% noncontrolling interest per share reflecting the minority discount?

Goodwill shown on Acquirer’s balance sheet: From Eq. (12.2), goodwill (FMVGW) can be estimated as follows:

FMVGW=(PP+FMV NCI)−(FMVTA−FMVTL)=($40,000,000+$10,000,000)−$42,000,000= $8,000,000

Goodwill attributable to the noncontrolling interest: Note that 20% of the total shares outstanding equals 200,000 shares, with a market value of $10 million ($50/share × 200,000). Therefore, the amount of goodwill attributable to the noncontrolling interest is calculated as follows:

Fair value of the Noncontrolling Interest per share: Since the fair value of Acquirer’s interest in Target and Target’s retained interest are proportional to their respective ownership interest, the value of the ownership distribution of the controlling (majority) and noncontrolling (minority) owners is as follows:

The FMV per share of the noncontrolling interest is $41.65 [i.e., ($10,000,000/200,000) × (1 − 0.167)]. The noncontrolling interest share value is less than the share price of the controlling shareholders (i.e., $50/share) because it must be discounted for the relative lack of influence of noncontrolling or minority shareholders on the firm’s decision-making process.

Exhibit 12.2

Guidelines for valuing acquired assets and liabilities

Cash and accounts receivable, reduced for bad debt and returns, are valued at their values on the books of the target on the acquisition/closing date.

Marketable securities are valued at their realizable value after transaction costs.

Inventories are broken down into finished goods and raw materials. Finished goods are valued at their liquidation value; raw material inventories are valued at their current replacement cost. Target last-in, first-out inventory reserves are eliminated.

Property, plant, and equipment are valued at the FMV on the acquisition/closing date.

Accounts payable and accrued expenses are valued at the levels stated on the target’s books on the acquisition/closing date.

Notes payable and long-term debt are valued at their net present value of the future cash payments discounted at the current market rate of interest for similar securities.

Pension fund obligations are booked at the excess or deficiency of the present value of the projected benefit obligations over the present value of pension fund assets. This may result in an asset or liability being recorded by the consolidated firms.

All other liabilities are recorded at their net present value of future cash payments.

Intangible assets are booked at their appraised values on the acquisition/closing date.

Goodwill is the difference between the purchase price and the FMV of the target’s net asset value. Positive goodwill is recorded as an asset, whereas negative goodwill (i.e., a bargain purchase) is shown as a gain on the acquirer’s consolidated income statement.

Table 12.5 illustrates the balance-sheet impacts of purchase accounting on the acquirer’s balance sheet and the effects of impairment subsequent to closing. Assume that Acquirer Inc. purchases Target Inc. on December 31, 2013 (the acquisition/closing date), for $500 million. Identifiable acquired assets and assumed liabilities are shown at their fair value on the acquisition date. The excess of the purchase price over the fair value of net acquired assets is shown as goodwill. The fair value of the “reporting unit” (i.e., Target Inc.) is determined annually to ensure that its fair value exceeds its carrying (book) value. As of December 31, 2014, it is determined that the fair value of Target Inc. has fallen below its carrying value, due largely to the loss of a number of key customers.

Table 12.5. Balance-Sheet Impacts of Purchase Accounting

FMV, Fair market value.

Asset-Liability Management (ALM) Risk

ALM risk is the potential loss in value of an institution's net asset value (the value of its assets minus the value of its liabilities) as a result of changes in market risk variables. For banks, this covers the interest-rate mismatch position between banking book assets and liabilities on the balance sheet, as well as the currency risk of any open currency position between assets and liabilities. For insurance companies and pension funds, ALM risk includes the risk that returns on the invested insurance premiums or pension contributions are less than expected and potentially insufficient to pay the expected insurance and pension liabilities.

A specific form of currency risk that is part of ALM risk is foreign exchange translation risk. This risk arises from an investment in a subsidiary that has revenues and costs primarily in a foreign currency. When reflecting earnings and capital of such a subsidiary in the financial accounts of the parent, changes in the exchange rate between the reporting currency of the parent and the foreign currency in which the subsidiary operates will change the subsidiary's contribution to earnings and capital.

Impact of purchase accounting on financial statements

A long-term asset is impaired if its fair value falls below its book or carrying value. Impairment could occur due to loss of customers, loss of contracts, loss of key personnel, obsolescence of technology, litigation, patent expiration, failure to achieve anticipated cost savings, overall market slowdown, and so on. In a case of asset impairment, the firm is required to report a loss equal to the difference between the asset's fair value and its carrying value. The write-down of assets associated with an acquisition constitutes a public admission by the firm's management of having overpaid for the acquired assets.

In an effort to minimize goodwill, auditors often require that factors underlying goodwill be tied to specific intangible assets for which fair value can be estimated, such as customer lists and brand names. These intangible assets must be capitalized and shown on the balance sheet. Consequently, if the anticipated cash flows associated with an intangible asset, such as a customer list, have not materialized, the carrying value of the customer list must be written down to reflect its current value.

13.3.2 Management fee

The management fee is due annually and is calculated as a percentage of the net asset value (NAV)a of the closed-end fund. However, the higher the management fee, the lower the amount of money left for investment activity. The percentage of the management fee is negotiated between LPs and GPs, since it is in the best interest of the investor to pay a lower percentage of fixed costs, while the opposite is true for GPs. This fee cannot be too low, because it is supposed to cover all operating costs incurred by the AMC. The management fee is a gross fee, since it covers operating expenses, pays the Advisory Company and the Technical Committee and fixed costs, and in the end the remunerationb for the AMC director. Average management fees vary from 1% to 3.5%. As a means of example, Fig. 13.2 reports the trend of the management fees for private equity fund manager in Luxembourg, a country that is headquarters of many private equity funds, as seen in Chapter 10. It can be seen that the average management fee decreased in the 3-year period. In 2017, approximately 50% of AMC were remunerated with more than 1.76% of management fees. On the contrary, in 2019, the percentage of managers remunerated with management fees larger than 1.76% is approximately 30%. This decreasing trend may be read along with the trend indicating that the average fund size enlarged in recent years. This may allow the same absolute remuneration with a lower percentage, leaving a larger portion of the fund to realize bigger scale investments.

8.6.1 Enterprise value

Enterprise value (EV) is the intrinsic value of the firm. It is the net asset value that is equal to the total assets less current liabilities. EV of a firm is an economic measure, which reflects the market value of the business. It is a fundamental metric in business valuation. It is the sum of the claims of both creditors and equity holders.

In general form, Enterprise value=Market value of equity+Value of debt.

The EV measures the value of the ongoing operations of a firm. EV can be considered as the theoretical takeover price of the firm. EV is an alternate to market capitalization.

Enterprise value=Market capitalization+Debt+Preferred share capital+Minority interest−Cash and cash equivalents.

3. The CPPI

The main advantage of the CPPI as a principal protection technique is that it gives a higher participation in the underlying asset than one can get from traditional capital protection. It also can be applied when interest rates are „too” low, or when options do not trade for some underlying risk. Before we discuss the CPPI algorithm and the associated risks we consider some market examples.

Example:

The CPPI investment is an alternative to standard tranche products, which offer limited upside (fixed premium) in exchange for unlimited downside (potential total loss of principal). CPPI offers limited downside (because of principle protection) and unlimited upside, but exposes investors to the market risk of the underlying default swaps contracts that comprise the coupon.

With yields hovering near record lows until recently, credit investors are increasingly moving to structures that contain some element of market exposure. That has posed a problem for ratings agencies, which are default oriented, and prompted a move to a more valuation-based approach for some products. Leveraged super senior tranches, also subject to market volatility, were the market-risk product of choice last year, but in recent months have ceded popularity to CPPI.

Banks profit from ratings on CPPI coupons because the regulatory capital treatment of rated products under Basel II is much kinder than on unrated holdings.

The CPPI is a structure which has constant leverage. Dynamic PPI is the name for strategies where the leverage ratio changes during the investment period. CPPI works by dynamically moving the investment between a safe asset and a risky asset, depending on the performance of the risky asset and depending on how much cash one has in hand. The main criteria in doing this is to protect the principal, while at the same time getting the highest participation rate.

The idea of CPPI can be related to the classical principal protection methods and is summarized as follows. In the classical principal protection the investor buys a zero coupon bond and invests the remaining funds to options. CPPI relaxes this with a clever modification. If the idea is to be long a bond with value 100 at T, then one can invest any carefully selected sum to the risky asset as long as one makes sure that the total value of the portfolio remains above the value of the zero coupon bond during the investment period. Then, if the portfolio value is above the value of the zero coupon bond, at any desired time the risky investment can be liquidated and the bond bought. This will still guarantee the protection of the principal, N. This way, the structurer is not limited to investing just the leftover funds. Instead, the procedure makes possible an investment of funds of any size, as long as risk management and risk preference constraints are met.

Let the initial investment of N be the principal. The principal is also the initial net asset value of the positions—call it Vt0. Next, calculate the present value of N to be received in T years. Call this the floor, Ft0.5

(6)Ft0=N(1+rt0)T

Let the increment Cut be called the cushion:

(7)Cut0=Vt0-Ft0

Then, select a leverage ratio λ in general satisfying 1 < λ. This parameter has no time subscript and is constant during the life of the structured note. Using the λ calculate the amount to be invested in the risky asset Rt0 as:

(8)Rt0=λ[Vt0- Ft0]

This gives the initial exposure to the risky asset St. Invest Rt0 in the risky asset and deposit the remaining Vt0 – Rt0 into a risk-free deposit account.6

(9)Dt0=Vt0-Rt0

Note that the cash deposit Dt0 is less than the time-t0 value of a risk-free zero coupon bond that matures at time T, denoted by B(t0,T)N, where B(t0,T) is the time t0 price of a default-free discount bond with par value $1. Hence, in case of a sudden and sizable downward jump in St, the note will not have enough cash in hand to switch to a zero coupon bond. This is especially true if the jump in St leads to flight-to quality and increases the B(ti, T) at some future date ti. This is called the gap risk by the structurers and is studied later in the chapter.

Apply this algorithm at every rebalancing date ti,

(10)ti-ti-1=δi

as long as Fti < Vti. This algorithm would increase the investment in the risky asset if things go well (i.e., if Vti increases), and decrease the investment in case markets decline (i.e., if Vti decreases).

Finally, if at some time τ* VT* falls and becomes equal to Fτ*, liquidate the risky investment position and switch all investment to cash. Since the floor Fti is the present value at ti, of 100 to be received at T, this will guarantee that principal N can be returned to the investors at T.

13.4 Pricing Efficiency Assessment

In this last section of the chapter, the pricing efficiency of iShares is examined. The pricing efficiency is assessed via the computation of the premium/discount in the trading price returns of iShares. The premium is calculated in percentage terms as the fraction of day’s t closing price minus the day’s t NAV for each ETF divided by the day’s t NAV. In addition, the persistence of premium is investigated by running a simple time series regression model of premium values on its one-day lagged values. This approach in assessing the persistence of premium has been found in Elton et al. (2002).

Table 13.5 reports the descriptive statistics of ETFs’ premium. In particular, the average and median premium of each ETF are presented along with the standard deviation of daily premiums (used to assess the volatility in premium) and the extreme scores, namely the lowest premium (i.e., discount) and the maximum premium observed for each ETF.

Table 13.5. Descriptive Statistics of Premium

Note: Negative premiums are named discounts.

This table presents the descriptive statistics of iShares’ premium as of 24 April 2013. Descriptive statistics include the average daily premium, the median premium, the standard deviation of premium’s values, and the extreme scores (minimum and maximum).

The results in Table 13.5 show that the average iShares trade at a significant premium to its NAV of 4.167%. This figure is quite higher than the average premiums of US-listed ETFs reported in the literature.9 The median premium is slightly better yet, but still high (it is equal to 3.849). The average standard deviation of premiums is equal to 3.792. This number is extremely high and indicates that there are a lot of fluctuations in terms of pricing behavior of Hong Kong iShares, whereby the latter inference is confirmed by the extreme scores. In particular, the average minimum discount of the sample is equal to 4.623%, whereas the average maximum premium equals the 14.715%.

The main inference drawn via the analysis of iShares’ premiums is that the specific ETFs deviate from what is the case for the majority of US-listed ETFs, whose premiums are usually low and very short-lived. The large premiums found in the pricing of Hong Kong iShares raise questions about the applicability of the efficient market hypothesis in the case of Hong Kong ETFs.

The regression results on premiums are provided in Table 13.6. The average beta estimate is equal to 0.976. All the single betas approximate to unity being statistically significant at the 1% level. This finding is indicative of high persistence in Hong Kong iShares’ premium from the day t − 1 to the day t. This finding contrasts the literature’s findings on US-listed ETFs.10 Persistence in premium may be related to statutory and other frictions that can make arbitrage execution less efficient.

Table 13.6. Premium Regression Results

This table presents the results of the premium’s regression on its one-day lagged values. Beta counts for the persistence in iShares’ premium. T-tests on alphas estimate the statistical significance of the difference of these coefficients from zero. T-tests assess the significance of the difference of estimates from zero. R-square assesses the explanatory power of the regression.