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Formula sheet/NISM Series X-A: Investment Adviser (Level 1)/Investment Products
[ INVESTMENT PRODUCTS ]

Derivatives: Futures Pricing & Spot-Futures Arbitrage

Futures Fair Value:F=Spot Price(S)+Carry Cost=S×[1+r×(t/365)]\text{Futures Fair Value}: F = \text{Spot Price} (S) + \text{Carry Cost} = S \times [ 1 + r \times (t / 365) ]
Basis:Basis=Spot Price−Futures Price(Contango:Basis<0;Backwardation:Basis>0)Basis: Basis = \text{Spot Price} - \text{Futures Price} (Contango: Basis < 0; Backwardation: Basis > 0)
Annualized Arbitrage Return(%):[(Futures Price−Spot Price)/Spot Price]×(365/Days to Expiry)×100\text{Annualized Arbitrage Return} (\%): [ ( \text{Futures Price} - \text{Spot Price} ) / \text{Spot Price} ] \times ( 365 / \text{Days to Expiry} ) \times 100
Option Payoffs:Call Buyer=max(0,ST−X)−C0∣Put Buyer=max(0,X−ST)−P0\text{Option Payoffs}: \text{Call Buyer} = max(0, S_{T} - X) - C_{0}\quad\Big|\quad \text{Put Buyer} = max(0, X - S_{T}) - P_{0}
Variables

If futures basis spread exceeds financing cost, cash-and-carry arbitrage (buy spot, sell futures) locks in riskless return. S: Spot price; F: Futures price; r: Financing / cost-of-carry rate; t: Days to expiry; X: Strike price; STS_{T}: Spot price at expiry; C0C_{0}, P0P_{0}: Option premium.

Worked examples
Economic Value Added (EVA) and Market Value Added (MVA)

Godrej Consumer reports EBIT of Rs 2,400 Cr, Effective Corporate Tax Rate of 25%, Total Capital Employed (Debt + Equity) of Rs 10,000 Cr, and Weighted Average Cost of Capital (WACC) of 11.5%. Total Market Capitalization of Equity is Rs 28,000 Cr, Market Value of Debt is Rs 2,000 Cr, and initial capital contributed by investors is Rs 6,000 Cr. Calculate EVA and MVA.

Semi-Annual Bond Pricing and YTM Calculation

An 8.0% p.a. coupon Government Bond has a Face Value of Rs 1,000, semi-annual coupon payments (Rs 40 every 6 months), and 4 years to maturity (8 semi-annual periods). If the market required Yield to Maturity (YTM) is 7.0% p.a. compounded semi-annually (3.5% per half-year), calculate the theoretical Bond Fair Price.

Macaulay Duration, Modified Duration & Price Sensitivity

A 3-year annual coupon bond with Face Value Rs 100 and coupon rate 8.0% trades at Par (YTM = 8.0%, Price = Rs 100). Cash flows: Year 1 = Rs 8, Year 2 = Rs 8, Year 3 = Rs 108. Compute Macaulay Duration, Modified Duration, and estimate the percentage price change if market yields increase by 75 bps (+0.75%).

Spot-Futures Arbitrage Return % Calculation

On 3rd March, Tata Steel spot shares trade on NSE at Rs 150.00. March futures expiring on 30th March (27 days to expiry) trade at Rs 152.00. Calculate the cash-and-carry arbitrage profit in Rs and express it as an annualized percentage return.