# LO 4.5: Describe how m apping o f risk factors can support stress testing.

LO 4.5: Describe how m apping o f risk factors can support stress testing.
If we assume that there is perfect correlation among maturities of the zeros, the portfolio VaR would be equal to the undiversified VaR (i.e., the sum of the VaRs, as illustrated in column 3 of Figure 5). Instead of calculating the undiversified VaR directly, we could reduce each zero-coupon value by its respective VaR and then revalue the portfolio. The difference between the revalued portfolio and the original portfolio value should be equal to the undiversified VaR. Stressing each zero by its VaR is a simpler approach than incorporating correlations; however, this method ceases to be viable if correlations are anything but perfect (i.e., 1).
Using the same two-bond portfolio from the previous example, we can stress test the VaR measurement, assuming all zeros are perfectly correlated, and derive movements in the value of zero-coupon bonds. Figure 6 illustrates the calculations required to stress test the portfolio. The present value factor for a one-year zero-coupon bond discounted at 3.5% is simply 1 / (1.035) = 0.9662. The VaR percentage movement at the 95% confidence level for a one-year zero-coupon bond is provided in column 5 (0.4696). Thus, there is a 95% probability that a one-year zero-coupon bond will fall to 0.9616 [computed as follows: 0.9662 x (1 – 0.4696 / 100) = 0.9616].
The VaR adjusted present values of zero-coupon bonds are presented in column 7 of Figure 6. The last column simply finds the present value of the portfolios cash flows using the VaR% adjusted present value factors. The sum of these values suggests that the change in portfolio value is \$2.67 (computed \$200.00 \$197.33). Notice that the \$2.67 is equivalent to the undiversified VaR previously computed in Figure 5.
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2018 Kaplan, Inc.
Topic 4 Cross Reference to GARP Assigned Reading – Jorion, Chapter 11
Figure 6: Stress Testing a Portfolio
Portfolio
CF
\$108.5
\$5 \$5 \$5 \$105
Year 1 2 3 4 5
Spot Rate 3.50% 3.90% 4.19% 4.21% 5.10%
PV(CF) \$104.83 \$4.63 \$4.42 \$4.24 \$81.88 \$200.00
VAR % 0.4696 0.9868 1.4841 1.9714 2.4261
P V
Factor 0.9662 0.9263 0.8841 0.8479 0.7798
VaR Adj. P V Factor 0.9616 0.9172 0.8710 0.8312 0.7609
N ew Zero
Value \$104.34 \$4.59 \$4.36 \$4.16 \$79.89 \$197.33
B e n c h m a r k i n g a P o r t f o l i o