- The Macaulay duration of the bond is the sum of the time-weighted present values ($477.7621) divided by the price (the $101.16 just being the sum of the present values)
times one plus half the yield, which is $100.2 (=101.16 × (1 + (1 + 2.092%/2). It can also be calculated directly as DV01 divided by the priceand is found to be 4.7702.- The Modified duration of the bond is found by dividing the Mac duration by one plus half the yield (4.772 / (1 + 2.092%/2) and is found to be 4.7208. It can also be calculated directly as DV01 divided by price and multiplied by 10,000: 0.0473/101.16*10,000 = 4.7208 (inputs rounded).
- The (Mac) convexity of the bond is approximately the sum of time squared weighted present values ($2347. 19) divided by price
times one plus half the yield($100.2) and is found to be 23.4354
Hi, I found some youtube videos on ULCi and spreadsheet on 2 asset ULC calculation. So please ignore the latter part of my comment. Thanks,Hi David,
On page 9 of the Study Notes for P1.T4 Schroeck's Chapter 14 on Capital Structure in Banks, under section "Describe how economic capital is derived",
"Step 3. Estimation of Unexpected Loss Contribution (ULC) to the lending portfolio as a function of expected loss, weight of the loan in the portfolio and its correlation with rest of the portfolio".
When I look at the formula for ULCi, I can see the weight of the loan, and the correlation to the portfolio, but I only see it as a function of unexpected loss of the loan to the portfolio, not expected loss.
Am not sure if it's a missed understanding on my part?
On a related note, do you publish videos or learning spreadsheet for Chapter 14 for P1.T4 or is it intentionally not produced? Always appreciate the rich learning content, so I thought I double check.
Thanks!
Evelyn
I am tagging to revise this for clarity, thank you!"Therefore, considering a loan at the portfolio level, the contribution of a single UL(i) to the overall portfolio risk is a function of:
- The loan’s expected loss (EL), because default probability (PD), loss rate (LR), and exposure amount (EA) all enter the UL-equation
- The loan’s exposure amount (i.e., the weight of the loan in the portfolio)
- The correlation of the exposure to the rest of the portfolio"