Chap 3 - Quantitative Foundations

Question 1

What is the classic yield and it’s formula ?

Answer 1

Definition : Rate of return at which an asset changes value

Return = ( Final value - Initial value ) / Initial value

Question 2

What is the notional yield and it’s formula ?

Answer 2

Definition : Yield calculation based on contract notional amount

Notional Yield = Change in value of contract / Notional Value

Question 3

What is the return based on fully collateralized position and it’s formula ?

Answer 3

Definition : Calculating the return on the combination of a contract and a hypothetical investment equivalent to the notional amount

Rfcoll = ln(1+R) + Rf

R = Change in value of contract, divided by preceding price or notional value

Question 4

What is the return based on partially collateralized position and it’s formula ?

Answer 4

Definition : Calculation of the return on the combination of a contract and a notional
percentage.

Rpcoll = [l * ln (1+R)] + Rf

1/l = Required ammount of collateral

Question 5

What is a Internal Rate of Return (IRR) and it’s types ?

Answer 5

Definition : Discount rate equivalent to the present value of cash inflows and outflows

Types of IRR:
* Lifetime
* Interim
* Since-inception

Question 6

What is a IRR - Lifetime ?

Answer 6

Definition : Contains all cash flows realized or anticipated over the life of the investment

Question 7

What is a IRR - Interim / Since-inception ?

Answer 7

Definition : Calculation of the internal rate of return before all cash flows are returned to the LP.

Question 8

What are the problems with IRR ?

Answer 8

Problems with the IRR :
* Potential multiple values fir the IRR
* Does not take investment size into
account
* Reinvestment assumption

Question 9

What is a IRR modified and it’s formula ?

Answer 9

IRR Modified :
* Solves the problem with multiple IRRs
* Rule for the reinvestment hypothesis
problem

MIRRt = (FV of positive cash flows at the reinvestment rate / -PV of negative cash flows at capital cost) ^ 1/t -1

Question 10

What is a Cascading cash distribution (Cash Waterfall) ?

Answer 10

Cascading cash distribution (Cash Waterfall)
* Limited Partnerships have provisions for the distribution of income between
General Partners (GP) and Limited Partners (LP).

Question 11

What are the Cascading cash distribution (Cash Waterfall) characteristics ?

Answer 11

• Performance fees
• Hurdle Rate
• Catch-up provision
• Clawback
• Vesting

Question 12

What are the performance fees in the cash waterfall distribution ?

Answer 12

Performance fees :

• Carried Interest: Private Equity I Real Estate
• Incentive Fee: Hedge Funds

Question 13

What are the distribution performance fees in the cash waterfall distribution ?

Answer 13

Distribution of performance fees :

• Fund-as-a-whole Carried Interest
• Deal-by-deal Carried Interest

Question 14

What is Clawback ?

Answer 14

Definition :

• Performance fees distributed to executives are reimbursed when a company
  incurs losses after profits.
• To ensure that the clause is respected, a percentage of the performance
  fee can be deposited in an Escrow account.

Question 15

What is a hard hurdle rate ?

Answer 15

Definition :
* Limits performance fees on profits in excess of hurdle rate

Example :
Let’s consider a 10M fund with a 20% performance fee that has generated 2M in profits. The
fund is subject to a 10% hard hurdle rate.

Question 16

What is a soft hurdle rate ?

Answer 16

Definition :
* Enables performance fees to be charged when the hurdle rate has been
exceeded on all profits.

Example:
Let’s consider a 10M fund with a 20% performance fee that has generated 2M in profits.
The fund is subject to a 10% soft hurdle rate.

Question 17

What simple interest and how does it work ?

Answer 17

Simple interest is an interest rate computation approach that does not
incorporate compounding. But returns are often compounded. For example, earning
10% over one year is equivalent to earning 9.64% per year compounded quarterly:
[1 + (.0964∕4)]^4 = 1.10.

Question 18

What is continuous compounding and Discrete compounding ?

Answer 18

Continuous compounding assumes that earnings can be instantaneously reinvested to generate additional earnings. Discrete compounding includes any compounding interval other than continuous compounding such as daily, monthly, or annual.

Question 19

Define the internal rate of return (IRR) ?

Answer 19

The internal rate of return (IRR) can be defined as the discount rate that equates the present value of the costs (cash outflows) of an investment with the present value of
the benefits (cash inflows) from the investment. Using the terminology and methods
of finance, the IRR is the discount rate that makes the net present value (NPV) of an
investment equal to zero.

Question 20

What is a borrowing type cash
flow pattern ?

Answer 20

A borrowing type cash
flow pattern begins with one or more cash inflows and is followed only by cash outflows. An example of the borrowing pattern is when an investment such as a real
estate project is sold and leased back. The divestment generates current cash at the
cost of future cash outflows and may be viewed as a form of borrowing.

Question 21

What is a multiple
sign change cash flow pattern ?

Answer 21

A multiple
sign change cash flow pattern is an investment where the cash flows switch over time
from inflows to outflows, or from outflows to inflows, more than once. An example of a multiple sign change investment would be a natural resource investment
involving (1) negative initial cash flows from purchasing equipment and land to set
up an operation such as mining, (2) positive interim cash flows from operations, and
(3) negative terminal cash flows from ceasing operation and restoration expenses.

Question 22

In fact, the maximum number of possible IRRs is
equal to the number of sign changes. When more than one IRR is calculated, none of
the IRRs should be used. There is no easy way for the IRR model to overcome this
particular shortcoming.

Answer 22

True

Question 23

What is a Scale difference ?

Answer 23

Scale differences are when investments have
unequal sizes and/or timing of their cash flows. When comparing investments with
different scales, an investment with a higher IRR may be inferior to an investment
with a lower IRR.

Question 24

Why is modified IRR (MIRR) usefull ?

Answer 24

The modified IRR approach addresses the
challenges of multiple IRRs and the restrictiveness of the reinvestment assumption in the IRR approach by discounting all project cash outflows into a present value using
a financing rate, compounding all cash inflows into a future value using an assumed
reinvestment rate, and calculating the modified IRR as the discount rate that sets
the absolute values of that future value and that present value equal to each other.

To address this problem, the modified IRR (MIRR) imposes userspecified rates to compound all cash inflows forward to the project’s termination date
and discount all cash outflows back to the project’s inception date.

Question 25

However, the MIRR approach is viewed as having substantial disadvantages that
make it a rarely used approach relative to the IRR. Note that the values of CC and
RR chosen by the user drive the value of the resulting MIRR. For example, a high RR
combined with a low CC will cause the MIRR to be high by increasing the future
value of the distributions and lowering the present value of the contributions. So
unlike IRR, MIRR is driven by user-selected rates (RR and CC) that conceptually
are unrelated to the project.

Answer 25

True

Question 26

What are time-weighted returns and Dollar-weighted returns ?

Answer 26

1- Time-weighted returns are averaged returns that
assume that no cash was contributed or withdrawn during the averaging period,
meaning after the initial investment.

2- Dollar-weighted returns are averaged returns
that are adjusted for and therefore reflect when cash has been contributed or withdrawn during the averaging period. The IRR is the primary method of computing a
dollar-weighted return.

Question 27

What is a hurdle rate ?

Answer 27

A hurdle rate specifies a return level that LPs must receive before GPs begin to
receive incentive fees. When a fund has a hurdle rate, the first priority of cash profits
is to distribute profits to the LPs until they have received a rate of return equal to the
hurdle rate. Thus, the hurdle rate is the return threshold that a fund must return to the
fund’s investors, in addition to the repayment of their initial commitment, before the
fund manager becomes entitled to incentive fees.

Question 28

What is a catch-up provision ?

Answer 28

A catch-up provision permits the fund manager to receive a large share of profits
once the hurdle rate of return has been achieved and passed. A catch-up provision
gives the fund manager a chance to earn incentive fees on all profits, not just the
profits in excess of the hurdle rate. A catch-up provision contains a catch-up rate,
which is the percentage of the profits used to catch up the incentive fee once the
hurdle is met. A full catch-up rate is 100%. To be effective, the catch-up rate must
exceed the rate of carried interest.

Question 29

What is Vesting ?

Answer 29

Vesting is the process of granting full ownership of conferred rights, such as
incentive fees. Rights that have not yet been vested may not be sold or traded by the
recipient and may be subject to forfeiture.

Question 30

What is a clawback clause ?

Answer 30

A clawback clause, clawback provision, or clawback option is designed to return
incentive fees to LPs when early profits are followed by subsequent losses. A clawback
provision requires the GP to return cash to the LPs to the extent that the GP has
received more than the agreed profit split. A GP clawback option ensures that if a
fund experiences strong performance early in its life and weaker performance at the
end, the LPs get back any incentive fees until their capital contributions, expenses,
and any preferred return promised in the partnership agreement have been paid.

Question 31

What is a compensation scheme ?

Answer 31

The compensation scheme is the set of provisions and procedures governing management fees, general partner investment in
the fund, carried-interest allocations, vesting, and distribution.

Question 32

The term carried interest tends to be used in private equity and real estate; the term incentive fee is more often used in hedge funds.

Answer 32

True

Question 33

Carried interest can be fund-as-a-whole carried interest, which is carried interest based on aggregated profits and losses across all the investments, or can be structured as deal-by-deal carried
interest. Deal-by-deal carried interest is when incentive fees are awarded separately
based on the performance of each individual investment.

Answer 33

True

Question 34

Explain the sequence of cash distributions of a hard hurdle rate:

Answer 34

The sequence of cash distributions with a hard hurdle rate is as follows:

1. Capital is returned to the limited partners until their investment has been repaid.
2. Profits are distributed only to the limited partners until the hurdle rate is reached.
3. Additional profits are split such that the fund manager receives an incentive fee
   only on the profits in excess of the hurdle rate.

Question 35

What is a soft hurdle rate ?

Answer 35

A soft hurdle rate allows fund managers to earn an incentive fee on all profits, given
that the hurdle rate has been achieved.

Question 36

Explain the sequence of cash distributions of a soft hurdle rate:

Answer 36

The sequence of cash distributions with a soft hurdle rate is as follows:

1. Capital is returned to the limited partners until their investment has been repaid.
2. Profits are distributed only to the limited partners until the hurdle rate is reached.
3. Additional profits are split, with a high proportion going to the fund manager
   until the fund manager receives an incentive fee on all of the profits.