Bonds with actual sovereign guarantee (GSECs) are currently yielding 7.3% - 8 %.

For an investment of **INR 10lac**,

the difference betweenâ€¦

- annual returns from GSECs (7.3% - 8%)

and
- annual returns from this PSU AT-1 bond (9.34%)

â€¦turns out to be **INR 15-20K**.

Thinking of these reduced returns as an **insurance**

to guarantee that nothing happens to the 10lac principal invested,

15K each year to insure 10lac is a very reasonable cost, right?

**Why bother with all the risks associated with an AT-1 bond ?**

If one already has a couple of crores invested in GSECs,

and can afford to risk occasionally losing dividend-returns or even the principal itself,

then can take a chance with 1-2 lots (10-20lacs worth) of such corporate PSU / NBFC AT-1 bonds, maybe?

Right.

I donâ€™t know the odds of this happening with SBI.

However, hereâ€™s what i knowâ€¦

If i were to purchase 1 lot of this SBI AT-1 bond,

- Winning scenario = i win 15K (increased dividend returns compared to GSECs)
- Losing scenario = i lose 10Lac (principal lost)

i.e. it is like an exciting lottery ticket that costs 10L, with a prize-money of 10.15L.

*(compared to putting the same 10L into some â€śboringâ€ť GSECs)*

Calculating the EV (Expected Value) associated with this â€ślottery-ticketâ€ť,

```
EV = (Probability of Winning) x (Amount Won) â€“ (Probability of Losing) x (Amount Lost )
EV = (( p ) * (15,000)) - ((1 - p) * (10,00,000))
```

where p is the probability of SBI NOT defaulting on these AT-1 bonds,

i.e. both paying out the annual dividends at 9.34% and not writing-off the principal amount.

The net result isâ€¦

```
EV = (10,15,000 * p) - 10,00,000
```

In the above equation, the **break-even** bet (EV = 0) is at p = 98.5

i.e. a positive EV requires p > 98.5

i.e. **a +EV bet requires the probability of SBI defaulting on these AT-1 bonds to be less than 1.5%**.

So, today one would invest in these AT-1 bonds

and expect to be better off than investing in GSECs today,

if the chances of SBI facing financial distress to the extent that they write-off these AT-1 bonds,

**are lower than 1.5%**.

NOTE: A more accurate EV can be calculated by including the other outcomes in the above equation.

*(eg. the possibility of not receiving dividend in a particular year, but the principal amount invested in the bond not being written-off either)*

PS: Also, anyone interested in estimating the probability/odds of rare events,

do checkout **Neglect of probability - Wikipedia**,

and adjust accordingly to account for one of the common biases in estimating rare events / extreme probabilities.

PPS: If one is good at estimating odds of rare events (a huge IF),

and is comfortable risking huge sums to earn a tiny return (but repeatedly and consistently over time),

i hear that **selling options** is something that one will likely enjoy.