Description: Measures the current value of a future cash flow
Keywords: Present Value, Time Value of Money, PV
Introduction
A given amount of money is more valuable today than at a future date. Present value is, therefore, the future value of a cash flow discounted by the time value of money. (Note that the Financial Instrument Technical Notes section of this guide provides details of valuing most instruments)
If one invests an amount of money, C, for t years at a rate of i% compounded annually, the present value of C, t years in the future is given by:
_{}
The expression _{} represents the present value of 1 and occurs in almost all present value calculations.
If interest rates are expected to change during t, it is also common to use these different interest rates for future time periods. For example, an investment over three years would have a present value (PV) of _{}, where t=3 and i=the annual rate of interest in each year.
The choice of interest rate is particularly important and this is typically, the risk free interest rate which is obtained from the rate of return of highly liquid sovereign debt, for example, US TBills. The risk free rate is used as a basis upon which to assess the risk of an investment: if the investment is “safe” it should perform at least as well as the riskfree rate, however if the investment contains some risk, this is reflected in a risk premium.
Importantly, present value is additive. The sum of the PV of each position in a portfolio equates to the PV of the portfolio as a whole.
Example
Assume the risk free rate to be 5.5% and a portfolio has two instruments within it
The present value of cash flow 1 is:
_{} = 973,584.77
The present value of cash flow 2 is:
_{} = 710,900.50
The present value of the portfolio is PV1 + PV2 = 973,584.77 + 710,900.50 = 1,684,485
Underlying Present
Value
Introduction
The
Underlying Present Value statistic
is very similar to Present Valuestatistic in that it defines a measure of worth for an instrument or portfolio.
However, the current Present Valuestatistic for some twolegged instruments can often be zero or near zero. While
this is correct, it does not always provide an intuitive sense of the “size” of
a position. For some instruments, one leg may be much more important than the
other; in which case we can take the “present value” of only that leg as
indicative of the true size of the position. We call this the Underlying Present Value.
For
example, an equity index future will have a present value equal to zero since
the futures contract is markedtomarket daily.
However, the underlying present value will represent how much of the
market you are invested in. For the
S&P 500 index futures, the contract specifications for the ‘big’ contract
are 250 times the index. This means that
the underlying present value will show that you are controlling 250 times the
current value of the S&P for each contract held.
For
FX forwards, the underlying present value will show that you are controlling
50MM Yen while the present value reports the marktomarket value which may be
a small amount.
For
singlelegged instruments Underlying
Present Value will simply be the same as Present Value. For some twoleggedinstruments. We cannot ascertain which leg is more important.
Underlying Present Value is useful as a
standalonestatistic as well as in conjunction with the Underlying Duration statistic defined in a previous specification.
Note that Underlying Present Valueis not meant to be a sensitivity measure but rather a value measure.
For options there is always the question of what the Underlying Price represents. RiskMetrics will report the option value when using the present value statistic. The underlying present value will report the delta adjusted amount of the underlying security you are controlling. If one has an option with a premium value of $1,000, the present value statistic will report $1,000. If the option was atthemoney on 1000 shares on a $20 stock, the underlying present value would be $10,000 (1000 x $20 * 0.5), where the ATM option delta is 0.5.
Definition of Underlying Present Value by Asset Type
Amortizing
Bond 
Same
as PV. 
Amortizing
Swap 
PV of the fixed leg only (including sign
based on pay/receives fixed). 
Bond 
PV of the bond only. Ignore the
settlement payment leg if it is present. 
Bond
Future 
PV of the bond leg only, ignoring the
“futures” payment. This can be computed exactly as market price*number of
contracts*notional/100.0. Note that sometimes the user specifies a
market price and other times it is left blank in which case RiskServer
computes one. 
Bond
Future Option 
PV of the bond leg only, ignoring all optionality. This can be computed exactly as
Underlying Price*Number of Contracts*notional/100.0. Preserve sign if
option type=call, reverse sign if option type=put. Note
that sometimes the user specifies an underlying price and other times it is
left blank in which case RiskServer computes one. Also note that Underlying
PV is not meant to be an “exposure” statistic, which is why delta is
ignored for option positions. 
Bond
Option 
PV of the bond leg only, ignoring all optionality and settlement. This can be computed
exactly as (underlying price+accrued_interest)*notional/100.0.
Preserve sign if option type=call, reverse sign if option type=put. 
Cap 
Unknown
at this time and waiting further research. For now simply set to PV. 
Floor 
Unknown
at this time and waiting further research. For now simply set to PV. 
Collar 
Unknown
at this time and waiting further research. For now simply set to PV. 
Cash 
Same
as PV. 
Cash
Flow 
Same
as PV. 
Commodity 
PV of the commodity only. Ignore
the settlement payment leg if it is present. 
Commodity
Option 
PV of the commodity leg only, ignoring
all optionality and settlement. This can be
computed exactly as underlying price*number of units. Preserve sign if option
type=call, reverse sign if option type=put. Note: I assumed that underlying price
is the spot price of the commodity. If this is not the case (i.e. It actually
represents the forward price at option expiry date) then we need to discount
the value above by the appropriate yield curve to get a true PV of the
commodity leg. 
Commodity
Future 
PV of the commodity leg only, ignoring
the “futures” payment. This can be computed exactly as market
price*number of contracts*number of units. 
Commodity
Future Opt 
PV of the commodity leg only, ignoring
all optionality. This can be computed exactly as
underlying price*number of contracts*number of units. Preserve sign if
option type=call, reverse sign if option type=put. 
Convertible
Bond 
PV of the convertible bond only. Ignore
the settlement payment leg if it is present. 
Equity 
PV of the equity only. Ignore the
settlement payment leg if it is present. 
Equity
Option 
PV of the equity leg only, ignoring all optionality and settlement. This can be computed exactly
as underlying price*number of shares. Preserve sign if option
type=call, reverse sign if option type=put. Note: I assumed
that underlying price is the spot price of the equity. If this is not
the case (i.e. It actually represents the forward price at option expiry date)
then we need to discount the value above by the appropriate yield curve to
get a true PV of the equity leg. 
Equity
Future 
PV of the equity leg only, ignoring the
“futures” payment. This can be computed exactly as market price*number of
contracts*number of shares. 
Equity
Future Opt 
PV of the equity leg only, ignoring all optionality. This can be computed exactly as underlying
price*number of contracts*number of shares. Preserve sign if option
type=call, reverse sign if option type=put. 
FRA 
Unknown
at this time and waiting further research. For now simply set to pv. 
FRN 
PV of the bond only. Ignore the
settlement payment leg if it is present. 
FX
Forward 
PV of the forward currency leg
only. Ignore the settle currency leg. 
FX
Option 
PV of the option currency leg only,
ignoring all optionality, settlement currency, and
settlement. This can be computed exactly as underlying price*notional.
Preserve sign if option type=call, reverse sign if option type=put.
Note: I assumed that underlying price is the spot price of the option
currency. If this is not the case (i.e. It actually represents the forward
price at option expiry date) then we need to discount the value above by the
appropriate yield curve to get a true PV of the option currency leg. 
Inflation
Indexed Bond 
PV of the bond only. Ignore the
settlement payment leg if it is present. 
Interest
Rate Future 
PV of the interest rate leg only,
ignoring the “futures” payment. We do not have a market price field,
but if we did the value we need would be computed as market price*number of
contracts*notional/100.0*time_factor, where time_factor is a fraction defined as term(in
months) divided by 12 months. For example, if the term is 3M then the time_factor would be 0.25. 
IR
Future Option 
PV of the interest rate leg only,
ignoring all optionality. This can be computed
exactly as underlying price*number of contracts*notional/100.0*time_factor, where time_factoris a fraction defined as term(in months) divided by
12 months. Preserve sign if option type=call, reverse sign if option
type=put. 
Money
Market Deposit 
PV of the underlying “bond” leg
only. Ignore the initial deposit leg if it present. 
MortgageBacked
Sec 
Same
as PV. 
Mutual
Fund 
PV of the mutual fund only. Ignore
the settlement payment leg if it is present. 
Overnight
Indexed Swap 
PV of the fixed leg only (including sign
based on pay/receives fixed). 
Swap 
Unknown
at this time and waiting further research. For now simply set to PV.
If we knew the swap was fixed for float than we could use the same rules as
for overnight indexed swaps and amortizing swaps. But this would not
help with fixed/fixed or float/float swaps. 
Swaption 
Unknown
at this time and waiting further research. For now simply set to PV
