Jenil Mehta
Keen member
Hi,
I am not able to understand the calculation for this part.
Can you please help me in understanding it.
I am not able to understand the calculation for this part.
Can you please help me in understanding it.
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SP5 September 2024 Q2iii
- Thread starter Jenil Mehta
- Start date
Colin McKee
Senior Member
There are quite a few calculations here. Can you indicate which parts of the examiners calculations you are struggling with and I can narrow it down a bit?
Jenil Mehta
Keen member
asset sales $60m of liabilities are sensitive to inflation
15 year liability duration => change in inflation of 0.01% => liability increase of 0.15% = $90,000
This part is understood
Calculation: 0.01%*60%*100mn*15 = 90000
change in inflation of 0.01% => £1m of inflation-linked government bonds increases by 0.20% = $2,000
This part I am not able to understand
What I interpret is that 0.01% inflation is multiplied with Inf bond term of 20yrs.
But why are we considering 1mn?
Because for liability we are considering 100mn.
=> invest 90,000 / 2,000 = $45m into inflation-linked government bonds 15 year liability duration
Wasn't able to interpret this
=> fall in interest rates of 0.01% => liability increase of 0.15% = $150,000
This part is understood
Calculation: 0.01%*100mn*15 = 150000
change in interest rates of 0.01% => $45m of inflation-linked government bonds increases by 0.20% = $90,000
Wasn't able to interpret this
fall in interest rates of 0.01% => $1m of fixed interest government bonds increases by 0.12% = $1,200
why are we considering 1mn?
=> invest ($150,000 - $90,000) / $1,200 = $50m into fixed interest government bonds
Wasn't able to interpret this
15 year liability duration => change in inflation of 0.01% => liability increase of 0.15% = $90,000
This part is understood
Calculation: 0.01%*60%*100mn*15 = 90000
change in inflation of 0.01% => £1m of inflation-linked government bonds increases by 0.20% = $2,000
This part I am not able to understand
What I interpret is that 0.01% inflation is multiplied with Inf bond term of 20yrs.
But why are we considering 1mn?
Because for liability we are considering 100mn.
=> invest 90,000 / 2,000 = $45m into inflation-linked government bonds 15 year liability duration
Wasn't able to interpret this
=> fall in interest rates of 0.01% => liability increase of 0.15% = $150,000
This part is understood
Calculation: 0.01%*100mn*15 = 150000
change in interest rates of 0.01% => $45m of inflation-linked government bonds increases by 0.20% = $90,000
Wasn't able to interpret this
fall in interest rates of 0.01% => $1m of fixed interest government bonds increases by 0.12% = $1,200
why are we considering 1mn?
=> invest ($150,000 - $90,000) / $1,200 = $50m into fixed interest government bonds
Wasn't able to interpret this
Colin McKee
Senior Member
The examiner considers 1m of I-L assets to establish how much 1m I-L bonds would increase if inflation moved 1/100th percent. But the key is that the examiner then uses that result to determine we would need 45m I-L bonds to hedge the liabilities. So the 1m is scaled up. (the 1m was just to get the sensitivity).
Then the examiner finds out the same information on 1m of fixed bonds (1,200). Finds out how much of the liability increase still has to be hedged after buying 45m of I-L bonds (150k - 90k) and then determines how many millions of fixed bonds we need to fill the gap (50m). I hope this helps,
Then the examiner finds out the same information on 1m of fixed bonds (1,200). Finds out how much of the liability increase still has to be hedged after buying 45m of I-L bonds (150k - 90k) and then determines how many millions of fixed bonds we need to fill the gap (50m). I hope this helps,
Jenil Mehta
Keen member
Got it
Thank you for explaining.
Thank you for explaining.
Eilidh Kerr
Made first post
Hi - I'm still struggling to understand this solution:
"15 year liability duration => fall in interest rates of 0.01% => liability increase of 0.15% = $150,000"
what is the logic behind this?
"15 year liability duration => fall in interest rates of 0.01% => liability increase of 0.15% = $150,000"
what is the logic behind this?
Colin McKee
Senior Member
Broadly, duration and modified duration are proxies for volatility, and we know volatility (V) = (-1/P)(dP / di) where P is price (ie value of 1m bonds). So rearranging, dP = (-V) * P * di = 15 * 1m * 0.0001 = 1,500. For 100m liabilities with 15 year term it would be 1,500 * 100 = 150,000.