Derivative instrument and Periodic yield: Difference between pages

Revision as of 22:14, 22 November 2015

Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.

Example 1

GBP 1 million is borrowed or invested.

GBP 1.03 million is repayable at the end of the period.

The periodic yield (r) is:

r = (End amount / Start amount) - 1

Which can also be expressed as:

r = (End / Start) - 1

or

r = <math>\frac{End}{Start}</math> - 1

= <math>\frac{1.03}{1}</math> - 1

= 0.03

= 3%

Example 2

GBP 0.97 million is borrowed or invested.

GBP 1.00 million is repayable at the end of the period.

The periodic yield (r) is:

r = <math>\frac{End}{Start}</math> - 1

= <math>\frac{1.00}{0.97}</math> - 1

= 0.030928

= 3.0928%

Check:

Amount at end = 0.97 x 1.030928 = 1.00, as expected.

Example 3

GBP 0.97 million is invested.

The periodic yield is 3.0928%.

Calculate the amount repayable at the end of the period.

Solution

The periodic yield (r) is defined as:

r = <math>\frac{End}{Start}</math> - 1

Rearranging this relationship:

1 + r = <math>\frac{End}{Start}</math>

End = Start x (1 + r)

Substituting the given information into this relationship:

End = GBP 0.97m x (1 + 0.030928)

= GBP 1.00m

Example 4

An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.

The periodic yield is 3.0928%.

Calculate the amount invested at the start of the period.

Solution

As before, the periodic yield (r) is defined as:

r = <math>\frac{End}{Start}</math> - 1

Rearranging this relationship:

1 + r = <math>\frac{End}{Start}</math>

Start = <math>\frac{End}{(1 + r)}</math>

Substitute the given data into this relationship:

Start = <math>\frac{1.00}{(1 + 0.030928)}</math>

= GBP 0.97m

Check:

Amount at start = 0.97 x 1.030928 = 1.00, as expected.

Effective annual rate

The periodic yield (r) is related to the effective annual rate (EAR), and each can be calculated from the other.

Conversion formulae (r to EAR and EAR to r):

EAR = (1 + r)ⁿ - 1

r = (1 + EAR)^(1/n) - 1

Where:

EAR = effective annual rate or yield

r = periodic interest rate or yield, as before

n = number of times the period fits into a calendar year

Periodic discount rate

The periodic yield (r) is also related to the periodic discount rate (d), and each can be calculated from the other.

Conversion formulae (r to d and d to r):

d = r / (1 + r)

r = d / (1 - d)

Where:

d = periodic discount rate

r = periodic interest rate or yield

Derivative instrument and Periodic yield: Difference between pages

Revision as of 22:14, 22 November 2015

Effective annual rate

Periodic discount rate

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@@ Line 1: / Line 1: @@
-''Risk management - hedging''.
+__NOTOC__
+Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.
-A derivative instrument or contract is one whose value and other characteristics are derived from those of another asset or instrument (sometimes known as the Underlying Asset).
-Derivative instruments are widely used by non-financial corporates for hedging purposes.
+<span style="color:#4B0082">'''Example 1'''</span>
+GBP 1 million is borrowed or invested.
-<span style="color:#4B0082">'''Example'''</span>
+GBP 1.03 million is repayable at the end of the period.
-A share option is a type of derivative contract, allowing the holder to buy shares at a certain predetermined strike price.
-The value of the share option derives from the current price of the related underlying share, relative to the option strike price.
+The periodic yield (r) is:
+r = (End amount / Start amount) - 1
-For instance, say we hold a call option to buy shares at a strike price of $50, and the option is very close to its expiry date.
+Which can also be expressed as:
-If the shares are trading at $90, our option to buy at $50 is valuable.
+r = (End / Start) - 1
-The option holder could exercise their option, paying $50 per share, and then sell the shares for $90 each, making a profit of $40 per share.
+''or''
-So the option itself is valuable.
+r = <math>\frac{End}{Start}</math> - 1
-We could sell the option for - roughly - $40 (per share).
+= <math>\frac{1.03}{1}</math> - 1
-On the other hand, if the share price were only $20, it wouldn't be rational to exercise an option to buy shares for $50.
+= 0.03
-It would be irrational to do that, because the shares are cheaper to buy in the market for $20 each.
+= '''3%'''
-Accordingly, the option isn't valuable at present.
+<span style="color:#4B0082">'''Example 2'''</span>
-The value of the option is being driven by - among other things - the share price.
+GBP  0.97 million is borrowed or invested.
+GBP 1.00 million is repayable at the end of the period.
-== See also ==
-* [[Call option]]
-* [[CCR]]
-* [[Collateral]]
-* [[Commodity risk]]
-* [[CP]]
-* [[Credit support annex]]
-* [[Embedded derivative]]
-* [[ETD]]
-* [[Expiry date]]
-* [[FC]]
-* [[Fixing instrument]]
-* [[Forward rate agreement]]
-* [[Futures contract]]
-* [[FVTOCI]]
-* [[FVTPL]]
-* [[Hedge fund]]
-* [[Hedging]]
-* [[Interest rate derivative]]
-* [[Interest rate swap]]
-* [[ISDA Master Agreement]]
-* [[Leverage]]
-* [[Margining]]
-* [[Mark to market]]
-* [[Maturity]]
-* [[Notional principal]]
-* [[Option]]
-* [[Outright]]
-* [[Potential Future Exposure]]
-* [[Replacement cost]]
-* [[Risk management]]
-* [[Rogue trader]]
-* [[Strike price]]
-* [[Tracker fund]]
-* [[Transfer]]
-* [[Underlying]]
-* [[Underlying asset]]
-* [[Underlying price]]
-* [[X-Value Adjustment]]  (XVA)
+The periodic yield (r) is:
-===Other links===
+r = <math>\frac{End}{Start}</math> - 1
-*[http://www.treasurers.org/node/8599  Masterclass: Derivatives, ''Sarah Boyce,'' The Treasurer]
-[[Category:Manage_risks]]
+= <math>\frac{1.00}{0.97}</math> - 1
+= 0.030928
+= '''3.0928%'''
+''Check:''
+Amount at end = 0.97 x 1.030928 = 1.00, as expected.
+<span style="color:#4B0082">'''Example 3'''</span>
+GBP  0.97 million is invested.
+The periodic yield is 3.0928%.
+Calculate the amount repayable at the end of the period.
+'''''Solution'''''
+The periodic yield (r) is defined as:
+r = <math>\frac{End}{Start}</math> - 1
+''Rearranging this relationship:''
++ r = <math>\frac{End}{Start}</math>
+End = Start x (1 + r)
+''Substituting the given information into this relationship:''
+End = GBP 0.97m x (1 + 0.030928)
+= '''GBP 1.00m'''
+<span style="color:#4B0082">'''Example 4'''</span>
+An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
+The periodic yield is 3.0928%.
+Calculate the amount invested at the start of the period.
+'''''Solution'''''
+As before, the periodic yield (r) is defined as:
+r = <math>\frac{End}{Start}</math> - 1
+''Rearranging this relationship:''
++ r = <math>\frac{End}{Start}</math>
+Start = <math>\frac{End}{(1 + r)}</math>
+''Substitute the given data into this relationship:''
+Start = <math>\frac{1.00}{(1  +  0.030928)}</math>
+= '''GBP 0.97m'''
+''Check:''
+Amount at start = 0.97 x 1.030928 = 1.00, as expected.
+====Effective annual rate====
+The periodic yield (r) is related to the [[effective annual rate]] (EAR), and each can be calculated from the other.
+'''''Conversion formulae (r to EAR and EAR to r):'''''
+EAR = (1 + r)<sup>n</sup> - 1
+r = (1 + EAR)<sup>(1/n)</sup> - 1
+Where:
+EAR = effective annual rate or yield
+r = periodic interest rate or yield, as before
+n = number of times the period fits into a calendar year
+====Periodic discount rate====
+The periodic yield (r) is also related to the [[periodic discount rate]] (d), and each can be calculated from the other.
+'''''Conversion formulae (r to d and d to r):'''''
+d = r / (1 + r)
+r = d / (1 - d)
+Where:
+d = periodic discount rate
+r = periodic interest rate or yield
+==See also==
+*[[Effective annual rate]]
+*[[Discount rate]]
+*[[Nominal annual rate]]
+*[[Nominal annual yield]]
+*[[Periodic discount rate]]
+*[[Yield]]
+*[[Forward yield]]
+*[[Zero coupon yield]]
+*[[Par yield]]
+===Other resources===
+[[Media:2013_09_Sept_-_Simple_solutions.pdf| The Treasurer students, Simple solutions]]