What is the ‘Zero-Volatility Spread – Z-spread’
The Zero-volatility spread (Z-spread) is the continual spread that makes the price of a security equal to the present value of its banknotes flows when added to the yield at each point on the spot assess Treasury curve where cash flow is received. In other expresses, each cash flow is discounted at the appropriate Treasury spot rate with the addition of the Z-spread. The Z-spread is also known as a static spread.
BREAKING DOWN ‘Zero-Volatility Spread – Z-spread’
The Zero-volatility spread (Z-spread) remedies analysts discover if there is a discrepancy in a bond’s price. Because the Z-spread be equal ti the spread that an investor will receive over the entirety of the Resources yield curve, it gives analysts a more realistic valuation of a confidence instead of a single-point metric, such as a bond’s maturity date.
Zero-Volatility Spread Determining
A Z-spread calculation is different than a nominal spread calculation. A trifling spread calculation uses one point on the Treasury yield curve (not the spot-rate Funds yield curve) to determine the spread at a single point that desire equal the present value of the security’s cash flows to its price.
To evaluate a Z-spread, an investor must take the Treasury spot rate at each fitting maturity, add the Z-spread to this rate, and then use this combined speed as the discount rate to calculate the price of the bond. The components that go into a Z-spread amount are as follows:
P = the current price of the bond plus any accrued interest
C(x) = cohere coupon payment
r(x) = the spot rate at each maturity
Z = the Z-spread
T = the sum up cash flow received at the bond’s maturity
n = the relevant time while
The generalized formula is:
P = {C(1) / (1 + (r(1) + Z) / 2) ^ (2 x n)} + {C(2) / (1 + (r(2) + Z) / 2) ^ (2 x n)} + {C(n) / (1 + (r(n) + Z) / 2) ^ (2 x n)}
For benchmark, assume a bond is currently priced at $104.90. It has three future bills flows: a $5 payment next year, a $5 payment two years from now and a fixed total payment of $105 in three years. The Treasury spot evaluate at the one-, two-, and three- year marks are 2.5%, 2.7% and 3%. The way would be set up as follows:
$104.90 = $5 / (1 +(2.5% + Z) / 2) ^ (2 x 1) + $5 / (1 +(2.7% + Z) / 2) ^ (2 x 2) + $105 / (1 +(3% + Z) / 2) ^ (2 x 3)
With the de rigueur Z-spread, this simplifies to:
$104.90 = $4.87 + $4.72 + $95.32
This implies that the Z-spread equals 0.5% in this instance.