Risk Management and Value Creation in ... - Arabictrader.com

Capital Structure in Banks 233
σ
E
2
= σ ⋅52 (5.62) 460
E,
W
As defined above, we use as a starting point for the iterative procedure:
V A
′ = DP ′ + V E
and σ A
= σ E
/4
We then proceed by iterating on Equations (5.52) and (5.53) until the
inferred values deviate from the observed input values less than ε = 0.01%.
The results for V A
and σ A
are shown in Table 5.5.
In order to calculate the distance to default (DTD), we first need to
determine the implied default probabilities. For Deutsche Bank, we use the
long-term senior debt rating from Standard & Poor’s and the results from
Brand and Bahar. 461 By using an exponential regression on the S&P default
observations, we can infer the following equation from mapping rating [AAA;
CCC] to numbers [1; 18]: 462
PD = 0.004%⋅e (0.4699⋅Rating-Number) (5.63)
Smoothing the results, we can derive the results shown in Table 5.6.
By applying the inverse standard normal function, we arrive at the results
shown in Table 5.7.
Setting the market risk premium equal to 6% and estimating β (from
the same weekly returns as σ E
) and s (the bond spreads above the risk-free
rate 463 ), we can estimate µ, the market value weighted average costs of capital,
as shown in Table 5.8.
And we finally arrive at the results shown in Table 5.9.
Table 5.5
Iterative Procedure
1999 1998
Input
V E
52.0 35.6
DP ′ 809.0 620.0
σ
1
E
37.0% 41.5%
Output from iterative module
V A
821.530 625.329
σ A
2.35% 2.38%
1 Note:The actual results were rounded (37.1% and 41.7%).
460 This formula assumes a constant volatility over time.
461 See Brand and Bahar (1999), p. 15. Since the two authors are with S&P, the results
should be consistent.
462 Obviously, this is only a shortcut for deriving exactly calibrated results.
463 We used again Bundesbank (2000), p. 51, for a rough estimate that is not exactly
trimmed to Deutsche Bank bond issues.