## How to calculate returns on government securities?

**T-bills -**

There are three T-bills variants and they vary based on the maturity period. They are 91 days, 182 days, and 364 days. T-bills do not carry an interest component, in fact, this is one of the biggest difference between T-bills and Bonds. T-bills are issued at a discount to their true (PAR) value and upon expiry, its redeemed at its true value.

__For ex -__consider a 91-day T-bill. Assume the true value (also called the Par value), is Rs.100. This T-bill is issued to you at a discount to its par value, Say Rs.97. After 91 days, you will get back Rs.100 and therefore you make a return of Rs.3. Think of it, this is as good as buying a stock at Rs.97 and selling it after 91 days at Rs.100. The only difference is that this is a guaranteed transaction, meaning, there is no risk of you selling below 100 (or above 100).

Yield essentially measures the return on your investment on an annualized basis. After all, all investments should be measured by its returns on an annualized basis. So if you have made 3 bucks over 91 days on an investment of Rs.97, then at this rate, how much would you have made on a yearly basis?

The formula is –

**Yield = [Discount Value]/[Bond Price] * [365/number of days to maturity]**

= [3/97]*[365/91]

= 0.0309*4.010989

=12.4052%

So in other words, the T-bill offers a return on investment of 12.4052%, but since you held it for 91 days, you will enjoy this return on a pro-rata basis.

Typical 91-day yields are around 6-7.5%. Needless to say, the higher the yield, the better it is.

**Note:**All yields are annualized

**Bonds -**

Bonds differ from T-bills on 2 counts. Bonds have long-dated maturities and they pay interest twice a year. Every bond issued will have a unique name or symbol. The symbol contains all the information you’d need. For example here is a symbol – 740GS2035A, and here is what this really means –

Annualized interest – 7.40%

Type – Government Securities (GS)

Maturity – 2035

Issue – ‘A’ means its a fresh issue (don’t worry much about this, just be aware that this is NSE’s internal nomenclature for their own book-keeping)

This issue is expiring in 2035 or 17 years from now (we are in 2018). If you were to invest in this bond, you will receive 7.4% interest every year until its maturity in 2035. Please note, the interest will be paid semi-annually, so you will get 3.7% interest twice a year. Finally, upon maturity, you will also get back your principal amount.

Every bond has a Par value, of say Rs.100. When you invest in a bond, you usually invest either at a discount (ex: 98, 97 etc) or at par (100), or at a premium to par (101,102 etc). The price at which you invest in a bond depends on something called as an ‘auction process’.

Now, consider you invest in 700GS2020 (7% with a maturity of 2020 or 2 years from now) at a discount price of 98.4. Assume, you invested in 150 of these bonds, so you’d pay –

150*98.4

= Rs. 14,760/-

Time Period | Interest | Cash flow | Remarks |
---|---|---|---|

0 – 6 Months | 3.5% | 3.5% * 100 * 150 = Rs.525 | Half year interest |

6 months – 1 year | 3.5% | 3.5% * 100 * 150 = Rs.525 | Half year interest |

1 – 1.5 years | 3.5% | 3.5% * 100 * 150 = Rs.525 | Half year interest |

1.5 – 2 years | 3.5% | 3.5% * 100 * 150 = Rs.525 | Half year interest |

At Maturity (2 years) | Principal repayment at Par | 150 * 100 = 15,000 | Additional Rs.240 |

So on an investment of Rs.14,760/- you will earn –

525 + 525 + 525 + 525 + 15,000

= 2100 + 15,000

= Rs.17,100/-

If you do the math, the yield on this works out to approximately 7.88%. RBI has explained the calculation of yield here, do check

**this**if you are keen to know more.Refer to the

**G-Secs chapter**on Varsity for a detailed explanation.

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