9
where P
j
is the default probability at t
j
, B
j
is the price of the j
th
corporate bond and Gj is the price
of the Treasury bond promising the same cash flows as the j
th
corporate bond. α
ij
is the present
value of the loss in the event of default on the j
th
bond at time t
i
, relative to the value “the bond
would have if there were no possibility of default”. α
ij
is given by :
α
ij
= υ (t
i
) [F
j
(t
i
) – R
j
(t
i
)C
j
(t
i
)] (6)
where υ (t) is the present value of $1 received at time t with certainty, F
j
(t) is the forward price
of the j
th
bond for a forward contract maturing at time t assuming the bond is default–free (t<t
j
),
R
j
(t) is the recovery rate for holders of the j
th
bond in the event of a default at time t (t<t
j
), and
C
j
(t) is the claim made by holders of the j
th
bond if there is a default at time t (t<t
j
).
From the Bloomberg terminal, we can find all the bonds outstanding, their maturity dates,
price, yield and rating. We find 16 bonds outstanding for Ford. Since we are only interested in
the 5-year CDS, we identify the bonds whose time to maturity is the closest to 5 years (referred
to as “Bond A”) and the bonds that have a maturity date earlier than that of Bond A. All the
bonds included in our analysis are shown in Table 1.
[Insert Table 1 here]
We also use Bloomberg terminal to find the treasury bonds outstanding, their maturity
dates, coupons, quoted prices and yields. Information regarding treasury bonds is included in
Table 2, columns 1-5. Column 6 reports the zero-coupon rates we bootstrapped from the
information given in columns 1-5.
[Insert Table 2 here]
The 3-month Treasury bill that expires on 08/18/2016 has a price of 99.92625 per $100
face value. To find its continuously compounded yield, we use the formula: FV=PV × e
rt
. By
plugging in the values for PV and FV, we’ll find 100 = 99.92625×e
(90/365)r
. Solving the equation,