How are YTM, YTC and YTW calculated?

Using XIRR over the security's actual cash flows on their actual dates: the price paid today, each dividend or coupon on its pay date, and par (or the call price) at maturity or the call date. XIRR finds the annual rate r where

Σ cash flow / (1 + r)^(days / 365) = 0

YTW is the lowest of YTM, YTC and, for perpetual preferreds, Stripped Yield. Yield and Stripped Yield are not XIRR: they are the annual dividend over the price, with Stripped Yield first removing the dividend accrued since the last pay date.

Why is Quarba's YTM higher than Bloomberg's?

Both are the same return, stated differently. XIRR gives an effective annual yield (EAY). Bloomberg's standard YTM is a nominal rate, the bond-equivalent yield (BEY): the per-period rate times the payments per year, with no compounding. For a security paying n times a year:

EAY = (1 + BEY / n)^n − 1

An 8% BEY is 8.16% effective when paid semi-annually and 8.24% when paid quarterly, as most preferreds are. The gap grows with the yield and the payment frequency.

Does XIRR assume dividends are reinvested?

No, this is a common misconception. The yield is the discount rate that makes the present value of the cash flows equal the price; it says nothing about what you do with a dividend once paid. "Effective annual" describes how the rate is quoted, not a reinvestment assumption. See Magni and Martin, The two sides of the reinvestment assumption fallacy in IRR and NPV, The Engineering Economist (2025).

How is duration calculated?

Modified duration: the approximate percent change in price for a 1 percentage point change in yield.

• Term (bonds, term preferreds): Macaulay duration of the cash flows to maturity, or to the call date when the security has been called, divided by (1 + YTM).

• Perpetual: 1 / Stripped Yield, the duration of a dividend stream that never ends. When a call is the worse case (YTC below Stripped Yield), the duration of the cash flows to that call.

• Floating: once floating, the time until the rate next resets: the next dividend for a 3-month SOFR floater, the next reset date for a 5-year reset. Before it floats, the duration of the fixed cash flows to the floating start date, since the coupon moves to market from there.

How is Projected Reset Yield calculated?

It is the yield at the next projected coupon for a floating, reset, or fixed-to-float security, including one still paying its fixed coupon:

reset coupon = projected index rate + index adjustment + spread

Projected Reset Yield = reset coupon × par / price

• Projected index rate: the market forward rate for the reset date, the first floating date for an issue still fixed and the next reset date otherwise. If a forward rate is not available, uses the current index rate.

• Index adjustment: 0.26161% for former 3-month LIBOR issues that moved to SOFR, or the adjustment stated in the prospectus.

• Spread: the fixed spread from the prospectus. Any stated floor or cap applies to the reset coupon.

Like Yield, it is a running yield at that coupon, not a yield to maturity.

What are Spread, IPO Spread and Spread vs IPO?

Spread is YTW minus the Treasury yield matching the security's duration. It is left blank for issues already floating, mandatory convertibles, and a negative YTW.

IPO Spread is the coupon minus the Treasury yield on the day the issue priced, at the Treasury matching its effective duration at issue. Priced at par, a callable security is cut short by the call if yields fall and runs to maturity, or forever for a perpetual, if they rise, so its effective duration falls between the two. It is the price change for a 0.01% yield shift, pricing at the lower of the price to the first call and the price to maturity:

effective duration = (P(y − Δ) − P(y + Δ)) / (2 × Δ × P)

A 6.5% perpetual callable after 5 years has a duration of 4.3 to the call and 15.4 as a perpetuity, and an effective duration of 9.8, matched to the 10-year Treasury. A call less than a year after issue is ignored, and a fixed-to-float issue runs to its floating start date. It is left blank for an issue floating within a year of issue.

Spread vs IPO is Spread minus the spread at issue, each over its own matching Treasury, so the two can use different benchmarks (a 20-year at IPO, a 10-year today); positive means wider than at IPO. It is left blank when YTW is a YTC and the matching Treasury is shorter than at IPO, where the low yield reflects call risk rather than credit.