Skip to content
Rob's s1452 Notes

✏️ Bonds and SVB (Silicon Valley Bank)

🙋Hey Rob, Slightly tongue-in-cheek. I’m a little sad we don’t have a section today. I’ve been fascinatedby the SVB Bank run and was looking forward to an exciting conversationand your thoughts on if the bank should have done anything differently to manage its risk given its unique niche of funds.
Can we spend some time on it the next time we get together?
✔That’s a perfect question because it combines several things that we’ve covered heavily:

  1. Bond pricing and interest rate risk.
  2. Federal reserve policy.

✏️ Suppose you have 10 year US treasuries with a face value of $20B. Interest rates have been so low that we will assume that the coupon rate is 0. Suppose that similar bonds are earning .5% interest. How much are your bonds worth?

✔ Click here to view answer

PB = $20/(1+.5%)^10 = $19.03B  ✅

✏️ Next, suppose that the fed raises interest rates to fight inflation. Suppose the yield on the 10 year treasury rises to 3.5%. How much are your bonds worth? Did you make money or lose it? How much? Explain.

✔ Click here to view answer PB=$20(1+3.5%)10=$14.18BP_B = \frac{\$20}{(1+3.5\%)^{10}} = \$14.18B

Your portfolio of bonds has dropped in value from $19.03B to $14.18B. You have lost $19.03B - $14.18 = $4850 Million.  ✅

✏️ What percentage of the bonds’ value did the bonds lose? Do an exact calculation. After that, use Duration to estimate the percentage of the bonds’ value that they lost.

✔ Click here to view answer

Exact %ΔP = (new price - old price)/old price = (14.18-19.03)/19.03 = -0.2549 = -25.49% Next let’s find the approximate %ΔP using the duration. Because these are zero coupon bonds, the duration is 10 years.

%ΔP≈−DUR×Δi1+i=−10×3.5%−.5%1+.5%=−29.85%\begin{aligned} \%ΔP &≈ -DUR × \frac{Δi}{1+i} \\ &= -10 × \frac{3.5\%-.5\%}{1+.5\%} \\ &= -29.85\% \end{aligned}

The duration formula was approximately correct, but because the interest rate change was so large, it wasn’t super accurate.  ✅