Summary FRM 1 BOOK 3 FORMULAE SHEET

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Ratio for insurance firm 1. 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑅𝑎𝑡𝑖𝑜: 𝑙𝑜𝑠𝑠 𝑟𝑎𝑡𝑖𝑜 + 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜
Use case:
Combined ratio is used to find 2. 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑅𝑎𝑡𝑖𝑜 𝑎𝑓𝑡𝑒𝑟 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠: 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑅𝑎𝑡𝑖𝑜 +
out total impact of loss ratio
and expense ratio. 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠
Note:
Multiple variation of same 3. 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜:
formula is possible. But basic
framework remains the same. 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑅𝑎𝑡𝑖𝑜 𝑎𝑓𝑡𝑒𝑟 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 – 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑖𝑛𝑐𝑜𝑚𝑒



Net asset value of fund 4. 𝑁𝑒𝑡 𝑎𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 ∶ 𝑁𝐴𝑉 =




m
Use case:
Calculation of net asset value
of mutual fund.




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Note:
You can expect direct
question on this concept.
Payoff of option 5. 𝐶𝑎𝑙𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑝𝑎𝑦𝑜𝑓𝑓: 𝐶 = 𝑚𝑎𝑥 (0, 𝑆 − 𝑥)
Use case:
5 Call option payoffs
6 Put option payoff.
fin
6. 𝑃𝑢𝑡 𝑜𝑝𝑡𝑖𝑜𝑛 𝑝𝑎𝑦𝑜𝑓𝑓: 𝑃 = 𝑚𝑎𝑥(0, 𝑋 − 𝑆 )

Using this combination of
du
formula, you can get question
on payoff calculation of
option strategy.
e

Note:
Payoffs can not be negative in
on


case of plain vanilla option
but it is possible in case of
barrier option.
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Forward contract payoff 7. 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑝𝑎𝑦𝑜𝑓𝑓: 𝑝𝑎𝑦𝑜𝑓𝑓 𝑝𝑎𝑦𝑜𝑓𝑓 = 𝑆 − 𝑘
Use case:
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Forward contract payoff 𝑊ℎ𝑒𝑟𝑒
calculation. 𝑆 = 𝑠𝑝𝑜𝑡 𝑝𝑟𝑖𝑐𝑒 𝑎𝑡 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦
𝑘 = 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 𝑝𝑟𝑖𝑐𝑒


Basis Risk 8. 𝑏𝑎𝑠𝑖𝑠 = 𝑆 − 𝐹
Use case: Finding basis of
forward/future contract. 𝑊ℎ𝑒𝑟𝑒
Note: Understand concept of 𝑆 = 𝑐𝑎𝑠ℎ (𝑜𝑟 𝑠𝑝𝑜𝑡) 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑢𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑎𝑠𝑠𝑒𝑡 𝑎𝑡 𝑡𝑖𝑚𝑒
widening of the basis risk, 𝐹 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑡