Day count conventions and Risk: Difference between pages

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The day count convention determines how interest accrues over time in a variety of transactions, including bonds, swaps, bills and loans. Interest is usually expressed to accrue at a rate per annum (the reference period). It is often due and payable at shorter intervals, usually a number of months (the interest period).
1. ''Corporate finance.''


The day count (or 'daycount') convention regulates how the parties are to calculate the amount of interest payable at the end of each interest or other period.  
In the corporate finance context, risk refers to the degree to which future returns may vary.


It is commonly expressed as a fraction. The [[numerator]] will be the convention for the number of days in the period - usually actual or a notional 30. The [[denominator]] is the convention for the number of days in the reference period - often 360 or 365.
Risk is often measured by the standard deviation of forecast returns.   
   
Conventions vary depending on the market type, location and the currency in question.


For example, euro-denominated bonds are usually calculated on an actual/actual basis, while fixed rate non-euro denominated bonds are often calculated on a 30/360 basis.  
It is often estimated by the standard deviation of <u>historic</u> returns, though this process is inherently error-prone when used for <u>forecasting</u> or for risk management purposes.


The London interbank market, on the other hand, operates on the basis of actual/360, except where the currency is sterling, for which the London interbank convention is actual/365 fixed.


2. ''Capital asset pricing model.''
Commonly used day count conventions are considered below, but first it is important to bear in mind the various business day conventions that may apply. These regulate the start and end date of each period.


==Business day conventions==
In the Capital Asset Pricing Model, relevant risk is measured by beta.


====No date adjustment====
Cycle dates are not adjusted for weekends or holidays and are forced to land within a cycle month.


====Following business day/next good business day====
3. ''Unknown occurrences.''
Dates are adjusted for weekends and holidays to the next good business day.


====Preceding/previous good business day====
In a more general sense, risk refers to the unknown (or unknowable) nature of future outcomes involving, for example, market prices or market rates.
Dates are adjusted for weekends and holidays to the previous good business day.


====Modified following/modified business day====
Dates are adjusted to the next good business day unless that day falls in the next calendar month in which case the date is adjusted to the previous good business day.


====End of month – no adjustment====
4. ''Adverse effects.''
Dates are adjusted to land on last day of the month.


====End of month – previous good business day====
Risk can also refer to the possibility of <u>adverse effects</u> resulting from:
Dates are adjusted to the last day of the month but if that day is a weekend or holiday, then it is adjusted backward to the previous good business day.


====Two business days prior to third Wednesday of month====
- Changes in market prices or rates, or
Dates generated are two business days prior to the third Wednesday of the month (used in conjunction with Eurodollar futures).


====Deposit rollover method====
- Changes in other general conditions in the market, or
Each date is set so it occurs on the same day of the month as the previous date. Each date is set to the next good business day but no
dates may be adjusted past the last good business day of the month.


==Day count conventions and conversions==
- Other economic factors specific to the business or other organisation (such as the failure of a key supplier).


Interest is calculated as the principal times the interest rate times the day-count fraction, where the day-count fraction is defined by the day-count convention associated with the interest rate.


====Money market basis (actual/360)====
5. ''Opportunity and hazard.''
This basis is commonly used for all Eurocurrency LIBOR rates, except sterling. The day count fraction is defined as the actual number of days in the period over 360.


====Actual/365 fixed====
More broadly, risk can refer to the possibility of any event occurring that will have an impact on the achievement of objectives.  
This basis is commonly used for all sterling interest rates, including LIBOR.  


The day count fraction is defined as the actual number of days in the period over 365.  
This includes both the upside opportunity and the downside hazard which could either move us towards or drive us away from achieving our objectives.  


It is also used for money markets in Australia, Canada and New Zealand.  
Risk in this context is measured both in terms of (1) its impact and (2) its likelihood.


This basis is sometimes confused with actual/365, which is defined next.


====Actual/365 or actual/actual====
==Treasury's role in risk management==
This basis is commonly used for all sterling bonds, Euro denominated bonds, US Treasury bonds and for some USD interest rate swaps.


In this case, the day-count fraction is the number of days in the period in a normal year over 365 or the number of days in the period in a leap year over 366.
No organisation can eliminate all risk, so risk has to be managed effectively. This is best done through a risk-aware culture.


====Eurobond basis (30E/360)====
Generally, treasury is about managing risk rather than taking risks.
30E/360 is used for calculating accrued interest on some legacy currency pre Euro Eurobonds and on bonds in Sweden and Switzerland.  


This method assumes that all months have 30 days, even February, and that a year is 360 days. Effectively if the start date d1 is 31 then it changes to 30, and if the second date d2 is 31 it too changes to 30.  
Many risks should be managed. Risk management is a key activity of the treasury function.


The day count fraction is defined as the number of days in the period (&Delta;<sub>360</sub>) over where (&Delta;<sub>360</sub>) is calculated as if every month had 30 days, as described in Figure 1.


[[File:Day count conventions figure 1.png||Bond basis (30/360) and Eurobond basis (30E/360)]]
== See also ==
 
* [[Agency risk]]
====Bond basis====
* [[Alienation of assets]]
This basis is used for calculating accrued interest on domestic US bonds (e.g. Yankee bonds, federal agencies, corporate and municipal bonds).
* [[Asset risk]]
 
* [[Basis risk]]
Each month is assumed to have 30 days, with an exception that if the last day is the 31st and the first day is not 30th or 31st then that month has 31 days.
* [[Beta]]
 
* [[Black swan]]
So the rule is if d1 is 31 it changes to 30, and if d2 is 31 change it to 30 but only if d1 is either 30 or 31.
* [[Business risk]]
 
* [[Call risk]]
====Floating rate notes====
* [[Capital asset pricing model]]
FRNs always use actual/360 or 365 in the case of sterling.
* [[Capital risk]]
 
*[[Cash]]
====Fixed coupon====
*[[Cash balance]]
This basis is commonly used for Eurobonds, and the day count fraction is just one divided by the number of interest payments per year. Thus the coupon payments are always the same and any small difference in the number of days between successive coupon payments is ignored.
*[[Cash flow]]
 
* [[Climate risk]]
====Conversion between different day count conventions====
* [[Commercial credit risk]]
 
* [[Commodity risk]]
[[File:Day count conventions figure 2.png||Conversion between different day count conventions]]
* [[Compliance risk]]
 
* [[Concentration risk]]
==Compounding conventions==
* [[Conduct risk]]
 
* [[Confiscation risk]]
====Simple interest====
* [[Counterparty risk]]
Simple interest does not offer the opportunity to earn interest on interest, ie, there is no compounding of
* [[Country risk]]
interest. Simple interest is typically used for instruments with a maturity of less than one year.
* [[Credit risk]]
 
* [[Currency risk]]
<math>Discount factor (DF) = \frac{1}{( 1+ R \times \frac{days}{year})}</math>
* [[Custody risk]]
 
* [[Cyber risk]]
where:
* [[Default]]
 
* [[Delivery risk]]
:'''R''' = simple interest rate on an actual/365 or actual/360 fixed basis
* [[Diversifiable risk]]
:'''days''' = number of days in period
* [[Diversification]]
:'''year''' = number of days in a conventional year (365 or 360)
* [[Documentation risk]]
 
* [[Downside risk]]
====Compound interest for multiple periods====
* [[Economic risk]]
Offers the opportunity for interest payments to be reinvested in order to earn interest on interest. Compound interest is typically used for instruments greater than one year.
 
<math>Discount factor (DF) = \frac{1}{(1+r)^{n}}</math>
 
where:
 
:'''r''' = periodic interest rate (<math>r = R \times \frac{days}{year}</math>)
:'''n''' = total number of compounding periods
 
====Continuous compounding====
Compounding can be taken to an extreme in which the interest is continuously compounded. Continuously compounded rates are rarely quoted in practice for outright deposits or borrowings, although they are used extensively in valuing options.
 
<math>Discount factor (DF) = e^{-Rt}</math>
 
where:
 
:'''R''' = continuously compounded interest rate per year;
:'''t''' = number of years to maturity; and
:'''e''' = 2.71828 (to five decimal places).
 
==Settlement day conventions==
 
The settlement day is the day on which traded bonds or securities actually change ownership and are paid for. This is often a few business days after the transaction date, T. Interest rate calculations normally start on the settlement day.
 
Settlement in Euro denominated bonds and in most markets is on T+3, although for US and UK government bonds and bills it is T+1, and for sterling bonds it is T+5.
 
 
==See also==
* [[Bond equivalent yield]]
* [[Compound interest]]
* [[Conventional year]]
* [[Day count]]
* [[Effective annual rate]]
* [[Effective annual rate]]
* [[Leap year]]
* [[Enterprise risk management]]
* [[LIBOR]]
* [[Environmental risk]]
* [[Money market yield]]
* [[Equity risk]]
* [[Nominal annual rate]]
* [[Equity risk premium]]  (ERP)
* [[Periodic discount rate]]
* [[Event risk]]
* [[Periodic yield]]
* [[Financial market risk]]
* [[Simple interest]]
* [[Financial market price risk]]
* [[Financial risk]]
* [[Fiscal risk]]
* [[Foreign exchange risk]]
* [[Franchise viability risk]]
* [[Funding risk]]
* [[Gap risk]]
* [[Geopolitical risk]]
* [[Guide to risk management]]
* [[Herstatt risk]]
* [[Inflation risk]]
* [[Insurance]]
* [[Insurance risk]]
* [[Interest rate risk]]
* [[Interest Rate Risk in the Banking Book]]
* [[Intraday risk]]
* [[Key risk indicator]]
* [[Legal risk]]
* [[Liquidity risk]]
* [[Market risk]]
* [[Market risk premium]]  (MRP)
* [[Market price risk]]
* [[Model risk]]
* [[Non-diversifiable risk]]
* [[Non-transferable risk]]
* [[Off balance sheet risk]]
* [[Operational risk]]
* [[Opportunity risk]]
* [[Option risk]]
* [[Pensions risk]]
* [[Pipeline risk]]
* [[Political risk]]
* [[Pre-transaction risk]]
* [[Prepayment risk]]
* [[Principal risk]]
* [[Rating risk]]
* [[Refinancing risk]]
* [[Regret risk]]
* [[Regulatory risk]]
* [[Reinvestment risk]]
* [[Replacement risk]]
* [[Reputational risk]]
* [[Response to risk]]
* [[Return]]
* [[Rewarded risk]]
* [[Risk analysis]]
* [[Risk appetite]]
* [[Risk averse]]
* [[Risk budget]]
* [[Risk evaluation]]
* [[Risk free]]
* [[Risk-free rates]]
* [[Risk free rate of return]]
* [[Risk identification]]
* [[Risk management]]
* [[Risk map]]
* [[Risk mitigation]]
* [[Risk policy]]
* [[Risk premium]]
* [[Risk register]]
* [[Risk reporting]]
* [[Risk tolerance]]
* [[Risk transmission]]
* [[Risk Weighted Assets]]
* [[Rollover risk]]
* [[Settlement risk]]
* [[Social risk]]
* [[Sovereign risk]]
* [[Specific risk]]
* [[Spread risk]]
* [[Spreadsheet risk]]
* [[Stranding risk]]
* [[Structural risk]]
* [[Systematic risk]]
* [[Systemic risk]]
* [[Systems risk]]
* [[Standard deviation]]
* [[Supply chain risk]]
* [[Tail risk]]
* [[Tax risk]]
* [[Transaction risk]]
* [[Transfer risk]]
* [[Transferable risk]]
* [[Transition risk]]
* [[Translation risk]]
* [[Treasury]]
* [[Treasury risk]]
* [[Uncommitted risk]]
* [[Unrewarded risk]]
* [[Value at risk]]
* [[Weather risk]]
* [[Wrong way risk]]
* [[Yield curve risk]]


[[Category:Long_term_funding]]
[[Category:Risk_frameworks]]
[[Category:Cash_management]]

Revision as of 01:19, 13 March 2023

1. Corporate finance.

In the corporate finance context, risk refers to the degree to which future returns may vary.

Risk is often measured by the standard deviation of forecast returns.

It is often estimated by the standard deviation of historic returns, though this process is inherently error-prone when used for forecasting or for risk management purposes.


2. Capital asset pricing model.

In the Capital Asset Pricing Model, relevant risk is measured by beta.


3. Unknown occurrences.

In a more general sense, risk refers to the unknown (or unknowable) nature of future outcomes involving, for example, market prices or market rates.


4. Adverse effects.

Risk can also refer to the possibility of adverse effects resulting from:

- Changes in market prices or rates, or

- Changes in other general conditions in the market, or

- Other economic factors specific to the business or other organisation (such as the failure of a key supplier).


5. Opportunity and hazard.

More broadly, risk can refer to the possibility of any event occurring that will have an impact on the achievement of objectives.

This includes both the upside opportunity and the downside hazard which could either move us towards or drive us away from achieving our objectives.

Risk in this context is measured both in terms of (1) its impact and (2) its likelihood.


Treasury's role in risk management

No organisation can eliminate all risk, so risk has to be managed effectively. This is best done through a risk-aware culture.

Generally, treasury is about managing risk rather than taking risks.

Many risks should be managed. Risk management is a key activity of the treasury function.


See also

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