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Formula sheet/NISM Series XV: Research Analyst/Terminology in Equity and Debt Markets
[ TERMINOLOGY IN EQUITY AND DEBT MARKETS ]

Macaulay Duration & Modified Duration

Macaulay Duration(DMac)=[∑(t×Ct/(1+y)t)+(n×M/(1+y)n)]/Current Market Price\text{Macaulay Duration} (D_{\text{Mac}}) = [ \sum ( t \times C_{t} / (1 + y)^{t} ) + ( n \times M / (1 + y)^{n} ) ] / \text{Current Market Price}
Modified Duration(DMod)=DMac/(1+y)  ⇒  %ΔPrice≈−DMod×Δy\text{Modified Duration} (D_{\text{Mod}}) = D_{\text{Mac}} / (1 + y) \;\Rightarrow\; \% \Delta Price \approx - D_{\text{Mod}} \times \Delta y
Variables

y: Yield per period (YTM); t: Time period of cash flow; ∆y: Change in interest rate/yield. CtC_{t}: Coupon cash flow at period t; M: Par / redemption maturity value; n: Total periods to maturity.

Exam note

Higher duration indicates higher interest rate price risk. Zero coupon bond duration equals its maturity (DMacD_{\text{Mac}} = n).

Worked examples
Standalone vs. Consolidated Enterprise Value (EV)

A parent entity has 2 Crore equity shares trading at Rs 450 per share. It has preferred capital of Rs 50 Cr, standalone debt of Rs 200 Cr, and standalone cash of Rs 60 Cr. Its subsidiary has minority interest of Rs 80 Cr, debt of Rs 120 Cr, and cash/liquid investments of Rs 40 Cr. Compute Standalone and Consolidated EV.

Bond Current Yield and Holding Period Return (HPR)

An 8.50% coupon G-Sec (Face Value Rs 100) is purchased in the secondary market at Rs 102.00. The investor holds it for 1 year, collects the annual coupon of Rs 8.50, reinvests the coupon at 6.00% p.a. for 1 year, and sells the bond at Rs 106.00. Calculate the Current Yield and the 1-year HPR.

Macaulay Duration, Modified Duration & Price Volatility

A 3-year annual bond with Face Value Rs 1,000 carries an 8% coupon and currently trades at par (Yield y = 8%). Its Macaulay Duration is calculated as 2.783 years. Calculate its Modified Duration and the expected % price change if interest rates increase by 75 basis points (+0.75%).