Types of G-Secs & Yield Calculations

Government Securities (G-Secs) are debt instruments issued by the Central and State Governments to finance fiscal deficits. They are considered risk-free as they carry sovereign guarantee. For bankers, G-Secs are important for SLR compliance, investment portfolio management, and treasury operations. This is a calculation-intensive topic in the JAIIB exam, requiring mastery of yield calculations, bond pricing, and duration concepts.

Government securities are tradeable debt instruments issued by the Government of India (or State Governments) acknowledging the government's debt obligation.

Key Features

• Sovereign guarantee: Zero default risk (risk-free)
• Minimum investment: Rs 10,000 (face value) and multiples of Rs 10,000
• SLR eligible: Count towards Statutory Liquidity Ratio
• Traded in secondary market: Through NDS-OM (Negotiated Dealing System - Order Matching)
• Regulated by: RBI (as the government's banker and debt manager)

1. Treasury Bills (T-Bills)

Short-term instruments issued at a discount to face value and redeemed at par.

Features:

• Issued at a discount and redeemed at face value (par)
• Zero coupon — no periodic interest payments
• The difference between purchase price and face value is the investor's return
• Auctioned by RBI on behalf of the Government
• Highly liquid and used for short-term investment

Discount yield on T-Bill: Yield = [(Face Value - Price) / Price] x (365 / Days to Maturity) x 100

Worked Example: T-Bill Yield

91-day T-Bill, Face Value = Rs 100, Purchase Price = Rs 98.50

Yield = [(100 - 98.50) / 98.50] x (365/91) x 100 = [1.50 / 98.50] x 4.011 x 100 = 0.01523 x 4.011 x 100 = 6.11% p.a.

2. Dated Government Securities (G-Secs / Bonds)

Long-term instruments with fixed or floating coupon payments.

Types of Dated Securities:

3. State Development Loans (SDLs)

• Issued by State Governments through RBI
• Similar to dated G-Secs but carry slightly higher yield
• SLR eligible
• Tenor usually 10 years
• Auctioned by RBI on behalf of State Governments

4. Sovereign Gold Bonds (SGBs)

• Issued by RBI on behalf of Government of India
• Denominated in grams of gold
• Minimum 1 gram, maximum 4 kg (individuals)
• Tenor: 8 years (exit option after 5th year)
• Fixed interest: 2.50% p.a. on initial investment, paid semi-annually
• Redemption price linked to gold price

The price of a bond is the present value of all future cash flows (coupons + face value at maturity).

Bond Price = Sum of [C / (1+r)^t] + [FV / (1+r)^n]

Where:

• C = Coupon payment (semi-annual: Annual Coupon / 2)
• r = Required yield per period
• t = Period number
• FV = Face value
• n = Total number of periods

Relationship Between Price and Yield

1. Current Yield

Current Yield = (Annual Coupon / Current Market Price) x 100

Simple measure that ignores capital gain/loss.

Example: Bond with Rs 80 coupon, trading at Rs 950 Current Yield = (80/950) x 100 = 8.42%

2. Yield to Maturity (YTM)

YTM is the total return expected if the bond is held to maturity, considering coupon payments AND capital gain/loss.

Approximate YTM = [C + (FV - P) / n] / [(FV + P) / 2] x 100

Where:

• C = Annual coupon
• FV = Face value
• P = Current market price
• n = Years to maturity

Worked Example: YTM

Bond: Face Value Rs 1,000, Coupon Rs 80, Price Rs 950, Maturity 5 years

YTM = [80 + (1000 - 950)/5] / [(1000 + 950)/2] x 100 = [80 + 10] / [975] x 100 = 90 / 975 x 100 = 9.23%

3. Yield to Call (YTC)

For callable bonds, calculated like YTM but using the call date instead of maturity date and call price instead of face value.

These are five fundamental theorems about bond price behaviour:

Theorem 1: Bond prices move inversely to bond yields. When yields rise, prices fall and vice versa.

Theorem 2: The increase in price when yield falls is greater than the decrease in price when yield rises by the same percentage (convexity effect).

Theorem 3: Longer maturity bonds have higher price sensitivity to interest rate changes.

Theorem 4: Between two bonds of the same maturity, the bond with the lower coupon experiences more price sensitivity than the one with a higher coupon.

Theorem 5: The sensitivity of a bond's price to yield changes increases at a diminishing rate as maturity increases.

Duration measures the sensitivity of a bond's price to changes in interest rates. It is the weighted average time to receive a bond's cash flows.

Macaulay Duration

Duration = Sum of [t x PV(CFt)] / Bond Price

Where t = time period, PV(CFt) = present value of cash flow at time t

Modified Duration

Modified Duration = Macaulay Duration / (1 + YTM/k)

Where k = number of coupon periods per year

Price Change = -Modified Duration x Change in Yield x Price

Factors Affecting Duration

CAPM calculates the expected return on an asset based on its systematic risk (beta).

Expected Return = Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)

Components

Worked Example: CAPM

Portfolio X: Beta = 1.2, Risk-free rate = 6%, Market return = 14%

Expected Return = 6% + 1.2 x (14% - 6%) = 6% + 1.2 x 8% = 6% + 9.6% = 15.6%

Portfolio Y: Beta = 0.8, Risk-free rate = 6%, Market return = 14%

Expected Return = 6% + 0.8 x (14% - 6%) = 6% + 6.4% = 12.4%

CAPM Assumptions

• Investors can borrow and lend at the same risk-free rate
• No taxes or transaction costs
• Markets are efficient and prices reflect intrinsic value
• All investors have homogeneous expectations

G-Secs are issued through auctions conducted by RBI:

Primary Dealers (PDs)

• Registered with RBI as licensed entities to buy and sell G-Secs
• Buy directly from RBI and resell to other buyers
• Create market liquidity for government securities
• System introduced by RBI in 1995
• Essential for the government's borrowing programme

• Any person resident in India — individuals, firms, companies, institutions
• State Governments, Provident Funds, Trusts
• NRIs, OCIs (Overseas Citizens of India)
• Foreign Portfolio Investors (FPIs) registered with SEBI and approved by RBI
• Foreign Central Banks (FCBs) under specific schemes

• G-Secs are risk-free sovereign instruments — minimum Rs 10,000 face value
• T-Bills: 91/182/364 days, issued at discount, zero coupon
• Dated Securities: 5-40 years, semi-annual coupon, fixed or floating
• SDLs: State Government bonds, SLR eligible, slightly higher yield than G-Secs
• T-Bill yield = [(FV - Price)/Price] x (365/days) x 100
• Current Yield = Annual Coupon / Market Price
• YTM = [C + (FV-P)/n] / [(FV+P)/2] — accounts for coupon + capital gain/loss
• Malkiel Theorem 1: Prices and yields move inversely
• Malkiel Theorem 3: Longer maturity = higher price sensitivity
• Malkiel Theorem 4: Lower coupon = more price sensitivity
• Higher YTM decreases duration — a common exam question
• Duration of a zero coupon bond equals its maturity
• CAPM: Expected Return = Rf + Beta x (Rm - Rf)
• Beta > 1: More volatile than market; Beta < 1: Less volatile
• Auctions: Multiple Price (each bidder pays own price) vs Uniform Price (all pay cut-off price)
• Primary Dealers create market for G-Secs; system introduced in 1995