Bond Valuation - CA Final SFM

Par Value

Par Value is the Face Value of Bond. If face value of bond is not given then face value can be assumed either Rs. 100 or Rs. 1000 or Rs. 10000 depending upon question.

Coupon Rate

Coupon Rate is the fix Rate of Interest which a bondholder receives as Interest Payment. Coupon Rate remains same until the bond matures.

Yield Rate

Current Yield/Yield Rate is Rate at which a bondholder receives as Interest Income on the Current Value of Bond.

Current Yield = Interest/Market Price of Bond

Yield to Maturity (YTM)

Yield to Maturity (YTM) is Rate of Earning if bond is held until Maturity. 

YTM = [(Interest + (Redemption Value (RV) - Net Proceeds (NP))/Maturity Period of Bond]/[(RV+NP)/2]

YTM = IRR can be used

Value of Bond

Value of Bond = ∑ PV of Interest Receivable + PV of Redemption Value

Value of Perpetual Bond = Interest/Yield Rate

Value of Bond if Company offers any Discount then

Value of Bond = Value of Bond As usual – Discount on Bond

Value of Discount on Bond

For 1^st Year = [1- 1/ (1 + Discount Rate)] x Face Value

For 2^nd Year = [1 – 1/ (1 + Discount Rate)²] x Face Value

And so on

If Redemption value of bond is not given then, face value of will be assumed as redemption value.

Yield to Call (YTC)

Return an Investor gets if bond is called after lock in period.

YTC = [(Interest + (Call Price – Market Price (MP))/Lock in Period of Bond]/[(Call Price +MP)/2]

Yield to Put (YTP)

Return an Investor gets if bond is retained after lock in period.

YTP = [(Interest + (Put Price – Market Price (MP))/Lock in Period of Bond]/[(Put Price +MP)/2]

Relation between Current Yield and Value of Bond – Bond Value Theorems

If Current Yield (Yield Rate) = Coupon Rate

Then Bond is selling at Par.

If Current Yield (Yield Rate) > Coupon Rate

Then Bond is selling at Discount.

If Current Yield (Yield Rate) < Coupon Rate

Then Bond is selling at Premium.

Forward Rate

Current Price = Interest₁/(1 + r₁) + Interest₂/[(1 + r₁) x(1 + r₂)] + .. +{Interest_n + Redemption Value}/[(1 + r₁) x…(1+ r_n)]

Commercial Paper

Effective Interest Rate = [(Redemption Value – Issue Price) x 100]/Issue Price

Stock Value of Bond = (No of Share per bond) x (Market Price per share)

Downside Risk

If the Actual Market Price of Assets (Bond) is greater than fundamental price then the Assets (bond) may correct i.e. there is probability of price going down.

Upside Premium

If the Actual Market Price is less than fundamental price then there is possibility of the price going up.

Downside Risk = [Market Price of Convertible Bond – Straight Value (Fundamental Value of Bond)] /Theoretical (Straight) Value of Bond

Conversion Premium = [(Market Price of Convertible Bond – Stock Value of Bond) x 100]/stock Value of Bond

Conversion Parity Price of Stock

Price of share is to be issued in lieu of convertible debenture (bond) such that there is no arbitrage opportunity to investor.

Conversion Parity Price = (Market Price of Convertible Bond)/No of Shares per Bond

Interest Rate Risk

Re – Investment Risk

It is the risk of interest rate falling because if the interest rate falls, then investor would able to re – invest the coupon amount at lower rate [Compounding Effect].

Price Risk

It is the risk of rising of Interest Rate because if the interest rate rises, then value of bond will fall [Discounting Effect].

So both the effects act in the opposite direction. They tends to cancel out each other and the period at which both cancels out each other is known as Macaqulay’s Duration.

So duration I that immunizing period at which re- investment effect cancel out the effect and realized yield is equal to promised by yield irrespective of interest rate changing.

Duration

Duration is nothing but the average time taken by an investor to collect his investment. If an investor receives a part of his investment over the time on specific intervals before the investment will offer him duration which would be lessor than the maturity of the bond.

Duration = ∑Wx/W

Where,

Wx = Weight x Discounted Annual Cash flows

W = value of Bond

Duration = [Current Yield x PVAF_{(YTM, n)} x (1 + YTM)]/YTM + [{1 – (Current Yield)/YTM) } x n]

If Bond Trades at par

Current Yield = YTM = Coupon Rate

Then

Duration = PVAF_{(YTM, n)} x (1 + YTM)

Duration of ZCB is the life of ZCB

Immunization Theorem

Duration of Liability = Duration of Assets

Duration of Portfolio = D_A x W_A + D_B x W_B

Price Volatility of Bond

Price Volatility of a bond is the sensitivity of bond price to the interest rate i.e. if interest rate changing by 1% then what would be % change in Bond Price.

Modified Duration = Duration/ (1+YTM)

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Interest Rate Swaps, Overnight Index Swaps, Cap, Floor and Collar Option - CA Final SFM

 Interest Rate Swaps

Interest Rate Swaps are the agreement between two parties to exchange payment obligation denominated in same currency. Interest Rate Swaps are based on Comparative Advantage Theory.

LIBOR = London Inter-Bank Offered Rate

MIBOR = Mumbai Inter-Bank Offered Rate

In Interest Rate Swaps parties agrees to borrow the money against their desire and exchange with each other to get the advantage of Interest deduction.

EC = Effective Cost of Interest in aggregate

Calculation of Effective Cost Payable by both parties and Saving to both parties due to swap     

Calculation of Interest Rate Payable by both parties		Calculation of Saving Due to Interest Rate Swaps
Interest Payment to Lender	XXX	EC Without Interest Rate Swap	XXX
Interest Payment to Party	XXX	EC With Swap Interest Rate Sap	(XXX)
Receive Interest Payment from Party	(XXX)	Intermediaries’ Share, if any	(XXX)
Effective Interest Cost to Party due to Swap	XXX	Saving available to distribute among Parties	XXX

     

Overnight Index Swaps (OIS)

Overnight Index Swaps is a type of swap in which one leg in MIBOR and another leg is fixed rate. MIBOR in OIS is compounded daily whereas fixed leg is not. In this swap one party receive fixed and pay floating, another party pay fix and receive floating. In case there is a Holiday than previous MIBOR of day on which holiday is assumed to previous day MIBOR without compounding.

Calculation of Fixed Interest Payment

Interest Received at floating rate	XXX
Add: - Any Payment on net settlement if any due to floating rate	XXX
Less: - Any Amount Received on net settlement if any due to floating rate	(XXX)
Expected Interest Rate Payment at Fixed Rate	XXX
Fixed Interest Rate = Expected Interest Payment at Fixed Rate    X 100                                                        Principal Convert Rate on Yearly Basis.

  

Cap, Floor and Collar Option

Cap

Cap is an option strategy that protects the borrower under a floating rate note from rise in Interest Rates. Individual option for Cap is known as Caplets.

In this type of option buyer of cap option agrees to pay fixed rate and receive floating by paying cap premium (i.e. Call Option).

Floor

Floor is an option strategy that protects the investor under a floating rate instrument from fall in interest rate. Individual option for Floor is known as Floorlets.

In this type of option buyer of floor agrees to pay floating and receive fixed by paying floor premium (i.e. Put Option).

Collar

Collar is a combination of a cap and a floor. In this strategy buy cap and sell floor. By taking collar floating rate borrower can reduce premium cost. 

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Derivative - CA Final SFM

Derivative include

Future: - Agreement to buy or sell a commodity or stock in future.

Forward: - Agreement to buy or sell a commodity or stock in future but traded Over The Counter (OTC) and actual execution of contract take place.

Option: - Right to buy or sell.

Option can be classified in two types

Call Option: - Right to Buy – (Up Side Batting)

Put Option: - Right to Sell – (Downside Batting)

Strike or Exercise Price

Strike or Exercise Price is Price at which contract will execute.

Option Premium or Option Price

Option premium is the cost for entering in to option contract. Option Premium is paid by buyer and received by writer.

Profit for buyer (Holder) is unlimited and loss is limited to premium paid.

Profit for Seller (Writer) is limited to premium received and unlimited loss.

Break Even Point

Breakeven is Gain from option is equal to premium paid.

BEP (Call Option) = Exercise Price (EP) + Premium Paid

BEP (Put Option) = Exercise Price (EP) - Premium Paid

BEP for Spread Strategy

BEP (where Call option is to be exercised) = EP + Cost of Strategy

BEP (where Put option is to be exercised) = EP - Cost of Strategy

Option Strategies

S. NO.	Name of Strategy	Explanation
1.	Long Straddle (C+, P+)	Buy Call & Buy Put at same strike price and for same maturity period. Investor Expects Market will be volatile in either direction
2.	Short Straddle (C- , P-)	Sell Call & Sell Put at same strike price and for same maturity period. Investor expects no volatile in the Market.
3.	Strip (2P+, C+)	Buy 2 Put & Buy 1 Call Option at same strike price and for same maturity period. Investor Expects market will more Bearish than Bullish.
4.	Strap (2C+, P+)	Buy 2 Call & Buy 1 Put Option at same strike price and for same maturity period. Investor Expects market will more Bullish than Bearish.
5.	Bull Call Spread (C+, C-)	Buy Call & Sell Call, Buy at Lower Rate and Sell at Higher Rate in Bullish Market. Premium for Long Call > Premium for Short Call. (Favorable Contract have higher premium)
6.	Bull Put Spread (P+, P-)	Buy Put & Sell Put, Buy at Lower Rate and Sell at Higher Rate in Bullish Market. Premium for Long Put < Premium for Short Put. (Favorable Contract have higher premium)
7.	Bear Call Spread (C-, C+)	Short Call & Long Call. Sell at lower and Buy at Higher in Bearish Market. Premium for Short Call > Premium for Long Call (Favorable Contract have higher premium).
8.	Bear Put Spread (P-, P+)	Short Put & Long Put. Sell at lower and Buy at Higher in Bearish Market. Premium for Short Put < Premium for Long Put (Favorable Contract have higher premium).
9.	Protective Put (S+, P+)	Long in Stock and Long in Put. Put acts as Insurance but Increase Cost of Acquisition.
10.	Covered Call (S+, C-)	Long in Stock and Short In Call. Call limits the upside but reduces the cost of Acquisition.

Intrinsic Value

Intrinsic Value is that part of the option premium which represents that extends to which the option is in the money. Intrinsic Value cannot be negative. If Option is At the Money or Out of the Money then there is no Intrinsic Value.

Time Value

Time Value is the difference between option premium and Intrinsic Value.  Time value falls with time and falls to zero on the expiration date.

Moneyness of the Option

S. No.	Scenario	Call Option	Put Option
1.	EMP = EP	ATM Indifference	ATM Indifference
2.	EMP > EP	ITM Exercise	OTM Lapse
3.	EMP < EP	OTM Lapse	ITM Exercise

  

Investment Value or Gross Profit = AMP – EP

Initial Margin

Initial Margin is the Initial Amount which is deposited by buyer and seller of future option. Initial Margin is the first line of defense for the Clearing House. It is also known as performance margin.

Maintenance Margin

Maintenance margin is the margin required to be kept by the investor in the equity account equal to or more than a specified percentage of Initial Margin.

Variation Margin

If the account balance goes below maintenance margin then investor needs bring in so much that Account balance again reaches Initial Margin Level, this is called Variation Margin.

Initial Margin = µ + 3σ         (µ = Average Change in the Value of Contract)

Maintenance Margin = Initial Margin x % required to be maintained

Arbitrage Profit

Arbitrage Profit = Riskless Profit

Arbitragers are the people who earn arbitrage profit due to difference in Actual Price and Theoretical Price.

Theoretical Future Price: -

Theoretical Future Price (TFP) is price calculated using cost of carry model. Cost of Carry Model means there should such relationship between spot price (Cash Market Price) and Future Price (Price in Derivative Market) that there should not arise no arbitrage profit.

          

S. No.	Cases	Non – Continues Compounding	Continues Compounding
1.	No Dividend Income	TFP = SP + COC	TFP = SP x ert
2.	Dividend Income	TFP = SP + COC – Dividend Income	TFP = (SP – PV of Dividend Income) x ert
3.	Dividend Yield is Given	TFPS = SP + COC – SP x Yield Rate	TFP = SP x e(r – y)t

Limitation of Arbitrage in Real Life

Transaction cost is ignored.

Margin Money is ignored.

Dividend Risk

Taxes are ignored.

Short selling is not allowed in Cash Market.

Basis = Spot Price - Future Price

Contango Market is such  a market in which the basis is decided solely by the Cost of Carry (COC).

Beta Management Using Index Future

Portfolio Managers generally do not sell their existing holding if they expects short term fluctuation in the market. Rather they would like to adjust their Portfolio Beta based on their assessment of any volatile movement in share market.

If portfolio manager expects that market will decline then –

He would like to decrease Portfolio Beta (Hedging).

If Portfolio Manager expects that market will rise then –

He would like to increase Portfolio Beta.

Hedging (Beta is also known as Hedge Ratio)

Existing Position	Future Position
Long in Stock (S+)	Short in Future (F-)
Short in Stock (S-)	Long in Future (F+)
No of Contract to be Bought or Sold = VP x (βD – βP)                                                               Nifty Future x Lot Size

Option Valuation

Binomial Model

Formula	Remarks
VOC = P x Cu + (1 – P) x Cd                            R	Where, R = 1 + Rf Cu = Call Upside Gain Cd =  Call Downside Gain Pu = Put Upside Gain Pd =  Put Downside Gain d = ds  (expected downside price divided by spot price)        s u = us  (expected upside price divided by spot price)        s
VOC = P x Pu + (1 – P) x Pd                            R
P = R – d        U – d
Value of American Option  =  Max of Discounted Value or Intrinsic Value

Put Call Parity Theory (PCPT)

Spot Price + Value of Put = Value of Call + Present Value of Exercise/Strike Price

PCPT is the relationship between European Call and Put Option on the same stock, the maturity period and EP is same.

The PCPT equation is made to prevent arbitrage profit. If LHS ≠ RHS, then there would arise arbitrage profit.

LHS Þ SP + VOP    (Protective Put – S⁺, P⁺)

RHS Þ VOC + PV of EP   (Fiduciary Call – C⁺, ZCB⁺)

Risk Neutral Valuation

The Price of an option is independent of the risk preference of Investor Called risk-neutral valuation.

Black Scholes Model

Formula	Remarks
European Call Option = SP x N (d1) – PV of EP x N (d2)	Where, Ln = Natural Log SP = Spot Price EP = Exercise Price R= Rate of Interest T = time
d1 = ln (SP) + (r + .5 σ2) x t               EP………………..                         σ√t
d2 = d1 -  σ√t
Assumption of Block Scholes Model European options are considered. No Transaction Costs. Short Term interest rates are known and constant. Stocks don’t pay dividend. Stock Price Movement is similar to random walk. Stock returns are normally distributed over a period of time. Variance of return is constant over the life of an option.

    

When Probability distribution or probable market price is given for market price of share on expiration then value of option will be calculated as follows: -

Value of Option = (AMP –EP) x Probability + (AMP – EP) x Probability + ……………….. (.i.e. we should check individually)

Future/(1 + R_f) = Spot Price + PV of Storage – PV of Convince Yield

Performance Analysis of Stock in terms of Percentage of Greeks

Delta

Delta is the degree to which an option price will move in given underlying stock price. A deeply out of the Money call will have a delta very close to zero and a deeply in the money call will have a delta very close to 1.

Gamma

Gamma measure how fast the delta changes for small change in the underlying stock price. It is the delta of the data.

Theta

The Change in Option Price on given day will decrease in the time to expiration. It is a measure of time decays.

Rho

The change in the option price a one percentage point change in the risk frees Interest Rate.

Vega

Vega is the Sensitivity of Option Value to Change in Volatility.

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