Carry
Gross Carry
The gross carry on an investment is the amount of passive income we expect to be earned from holding an investment. For bonds, carry is equal to the coupon rate. For equities, it is equal to the dividend yield.
No adjustment is made for credit risk. For a risky bond, we assume all coupon payment will be made in full.
For derivatives, the carry is equal to the carry of the appropriate replicating portfolio. For example, in theory, we can replicate a call option with an investment in the underlying security and a risk-free bond. For a call option, then, we set the carry equal to the carry from this equivalent replicating portfolio. Even though these replicating portfolios might be difficult to implement in practice, and even though the investor will not receive this carry explicitly, calculating carry in this way avoids any reporting arbitrage.
Net Carry
When finance professionals talk about carry, they are usually talking about the gross carry minus the cost of financing. To avoid any ambiguity, we refer to this as net carry.
It is often convenient to assume that the cost of financing is equal to the risk-free rate, but in practice the cost of financing will vary for different investments and for different borrowers. In a large portfolio, apportioning the cost of financing for individual securities can be extremely complicated.
While investors will ultimately want to know the net carry, because we typically do not know the cost of financing for any particular fund, Northstar reports the gross carry.
Gross Carry for Specific Security Types
Using the following notation,
c = coupon rate
D = dividend yield per annum, annual compounding
Δ = delta of an option
N = notional of bond
R = risk-free rate per annum, annual compounding
S = stock price (underlying stock price for option and forward)
V = fair value of an option
The gross carry, per year, in the local currency is equal to
Bond: N x c
Cash: V x R
Equity: S x D
Equity Option: (V − ΔS) x R + ΔS x D = ΔS(D − R) + V x R
Credit Default Swap: N x c (here, c is the coupon on the swap, not the underlying bond)
Contract for difference (CFD) or Equity Swap: S x (D − R)
Equity Index Forward: S x (D − R) / (1 + D)
By replacing D in the last equation with the negative of the cost of storage, or the foreign risk-free rate, we could calculate the gross carry for commodity forwards and FX forwards, respectively.