Risk-free rate
Also written Riskless rate · Sovereign rate
The rate on a sovereign borrowing in its own currency, where credit risk is absent because the government can print the money — the benchmark every other valuation is measured against.
In plain language
Lend to the Government of India in rupees and there is one risk you do not have: the risk of not being repaid. A sovereign borrowing in its own currency can always create the currency it owes. The rate on that borrowing is therefore the rate with no credit risk in it, and that is precisely what "risk-free" means here — free of credit risk, and nothing more.
Every other borrower is priced off it. A lender to a company faces the possibility of default, so demands more, and the extra is the credit spread. Group borrowers by rating and the market quotes the spread rather than the rate: 10 basis points for AAA, 25 for AA, and so on over the same sovereign rate for the same term.
The workbook's framing is worth memorising: the risk-free rate is the opportunity cost of earning a return without risk, and therefore the benchmark for all valuation.
How it works
"Risk-free" is a narrower claim than it sounds, and the workbook is careful about it.
Credit risk is genuinely absent for a home-currency sovereign — though the text notes that governments have defaulted in emergencies, citing the 2008–2012 European debt crisis.
Market risk is not absent. A government bond's price falls when yields rise like any other bond. It disappears only if the investor holds to maturity and is redeemed at face value by the issuer.
Reinvestment risk is not absent either. It disappears only for a zero-coupon instrument, where there is no interim coupon to reinvest.
Put the three together and the workbook's conclusion follows exactly: buy a zero-coupon instrument with no embedded call, issued by a sovereign in its home currency, and hold it to maturity — and there is no risk at all. Only then is a fixed-income security also a fixed-return security.
This also explains why the G-Sec yield curve is described as delivering a public-good function: it is the ultimate risk-free proxy for the pure time value of money, and every riskier asset is priced at a spread over it.
The formula
Borrower's rate = Risk-free rate (same term) + Credit spread (that rating)
Required return on any asset = Risk-free rate + Risk premium
A worked example
The workbook's ladder. With a risk-free rate of 8.25%:
| Borrower | Credit spread | All-in rate |
|---|---|---|
| Sovereign | — | 8.25% |
| AAA | 0.10% | 8.35% |
| AA | 0.25% | 8.50% |
Twenty-five basis points looks trivial. On Rs 1,000 crore of five-year borrowing it is Rs 2.5 crore a year, Rs 12.5 crore over the life of the issue — bought purely with a credit rating.
Where a bond desk meets it. A treasury is offered a 5-year AA corporate bond at 8.50% while the 5-year G-Sec yields 8.25%. The 25 bp is the entire compensation for taking default risk, illiquidity and a wider bid-offer. On Rs 50 crore that is Rs 12.5 lakh a year. If the issuer is downgraded to A and the market spread widens to 60 bp, the bond reprices to yield 8.85%; with a modified duration of 4.1 that is a mark-to-market loss of:
0.35% × 4.1 × Rs 50 crore = Rs 71.75 lakh
Nearly six years of the spread, wiped out by one notch of rating. The spread is compensation for exactly this.
The complete no-risk case. A 91-day Treasury bill bought at Rs 99.6898 with 34 days to run and held to redemption at Rs 100. No coupon to reinvest, no credit risk, no market risk once held to maturity. The 3.34% bond equivalent yield is realised in full — the only construction in the paper where the return is genuinely certain.
Why NISM asks about it
Chapter 1, section 1.5, defines the risk-free rate through the absence of credit risk and builds the credit-spread ladder on it; the same section separates market risk and reinvestment risk and reaches the zero-coupon-held-to-maturity conclusion. Section 1.6 makes the risk-free curve the base of the term structure. Chapter 3, section 3.5, returns to it when explaining why the G-Sec yield curve needs a credible hedging instrument, and Chapter 4 lists the short-term risk-free rate as one of the five inputs to the Black-Scholes model.
Questions ask which risk the risk-free rate is free of, why a home-currency sovereign carries no credit risk, and how to build a corporate rate from a risk-free rate and a spread.
Common exam traps
- Risk-free means free of credit risk only. A G-Sec still carries market risk and reinvestment risk, and the exam tests this precise distinction.
- The currency matters. A sovereign borrowing in a foreign currency cannot print it, so that borrowing is not risk-free.
- Match the term. A 5-year corporate bond is priced over the 5-year sovereign rate, not the overnight one; there is a risk-free rate for every tenor.
- Risk-free is not risk-less in every state. The workbook cites the European debt crisis to make the point that sovereigns have defaulted.
- Only the full construction removes all risk — zero coupon, no embedded call, home-currency sovereign, held to maturity. Drop any one condition and a risk returns.
- The spread is quoted, the rate is derived. Corporate markets quote the add-on over the benchmark, not an absolute rate.
Where this is taught
Free preparation for NISM Series V-DRelated terms
- Interest rate riskThe risk that an investor in a debt instrument loses return because rates rise — existing instruments carrying the old, lower coupon fall in value until their yield matches the new market rate.
- Reinvestment riskThe risk that the coupons or other intermediate cash flows from an investment have to be put back to work at a lower rate than the original investment earned, pulling the total return below the promised yield.
- Government SecurityA tradeable debt instrument issued by the Central Government or a State Government — treated as free of default risk, and the benchmark against which other rupee interest rates are priced.
- Credit spreadThe extra yield a non-government borrower must pay over a government security of the same tenor — the market price of credit risk, quoted as an add-on over the risk-free rate.
- Real interest rateThe nominal rate adjusted for inflation — what the lender actually gains in purchasing power, and a number that turns negative whenever inflation runs above the coupon.
- Spot rateThe true return on money invested today for one stated term with no interim cash flow — read straight off a zero-coupon instrument, and the only rate a cash flow should be discounted at.
- Term structure of interest ratesInterest rate plotted against term — one curve per credit quality, with the risk-free curve as the base and every other borrower quoted as a spread over it.
- Fisher effectThe proposition that, other things equal, a rise in expected inflation raises the nominal interest rate — which is why interest rate derivatives are the household sector's instrument for hedging inflation.
- RhoThe option Greek that measures interest rate sensitivity — the change in an option premium for a one percentage point change in the risk-free rate. It is positive for calls and negative for puts.
- Binomial pricing modelAn option pricing model that maps the underlying's possible prices as a tree of up and down moves at equally spaced time steps — accurate and flexible because it is iterative, but slow to compute.
- Overnight MIBORThe benchmark overnight rupee interbank rate administered by FBIL, and the underlying of India's money market interest rate futures contract, which is quoted as a rate rather than a price.