More "Exotic" Greeks in Convertibles

When contemplating the more exotic greeks relating to convertibles, you want to think about dividend and credit risk.

Phi (Dividend Risk)

Sensitivity of CB value to a change in dividends (or rather the dividend yield). The relationship between fair value and dividend yield is an inverse one.

CB value (simplified equation) = [PV of the CB's income - PV of stock dividend over the expected life of the security].

If you're long CB, you're long an option on stock, so without holding the stock you're not getting dividends. This can be a huge opportunity cost, thus dividend risk can be significant.

If I underestimate dividends, then I overestimate the value of the Convertible Bond.

Omicron (Credit Risk)

Sensitivity of the bond to change in credit spread. This can be the most important sensitivity measure for an OTM convertible. It's really, really important to know the omicron risk of your CB position and even more so for your portfolio as a whole.

This is particularly true for low-grade issues.

Generally speaking, as credit spreads narrow - this is good for the convertible's value. As credit spreads widen, this reduces the value of the convertible.

Greeks Needed for Convertible Arbitrage Purposes

DELTA (By that I mean the Continuous-Time Delta)

ANALYTIC DEFINTION- change in CB price for a given change in the Underlying Stock price.
MEANING - equity sensitivity for a CB.Tells the arbitrageur how many shares to SHORT against a long bond position.
CALCULATION - It's taken as N(d1) discounted by the stock's dividend yield.

NUMERIC RANGE OF DELTA:
* Approaches one as CB moves deep-in-the-money.
* Approaches zero as the stock price falls.

MORE ABOUT DELTA:
What we've talked about is the continuous-time delta. Suppose you expect to rebalance the hedge for every 5% move in the stock price - so you can calculate the change in value for a down move  and for an up move, average them, and that's your delta. It's still one number - but you factor in any asymmetric behaviours.

GAMMA

Sensitivity of delta to changes in Stock Price. A higher gamma implied the convertible's hedge must be rebalanced more frequently.

The interesting thing about gamma is it's variation with moneyness. Gamma is low for deep-in-the-money convertibles and for a far-out-the-money convertible. ATM CBs have the highest gammas.

Break-even Inflation - What it Means for Investors

You may have seen charts of the "break-even inflation" rate (% yield versus maturity) and wondered - what is this inflation rate represent?

Why does it vary with maturity, and maturity of what kind of product? What does it mean to say the B/E inflation rate in the US for April 2014 is 2%?

The Vanguard Group (an asset management firm) have published a tutorial on break-even inflation, and how it's derived, and how it's relevant to investment selection. It explains that B/E Inflation = Comparable Fixed Rate - Inflation-Linked Real Yield.

If BEI = 2%, then if average inflation is more than 2%, the inflation-linked investment will outperform the fixed rate investment.

The DVO1, or Delta, of a Bond

The DVO1, Bond Duration or "Delta" of a bond, describes how the bond price changes to a change in yield.