My Life

The Square Root of 3 by Dave Feinberg

Was watching Harold and Kumar: Escape. This poem is also read aloud by Kal Penn (Kumar):

I’m sure that I will always be,
A lonely number like root three,

The three is all that’s good and right,
Why must my three keep out of sight
Beneath the vicious square root sign,
I wish instead I were a nine,

For nine could thwart this evil trick,
with just some quick arithmetic,

I know I’ll never see the sun, as 1.7321,
Such is my reality, a sad irrationality,

When hark! What is this I see,
Another square root of a three

As quietly co-waltzing by,
Together now we multiply
To form a number we prefer,
Rejoicing as an integer

We break free from our mortal bonds,
With the wave of magic wands,

Our square root signs become unglued,
Your love for me has been renewed.

Credit Spreads Explained

Credit investors need a measure to determine how much they are being paid to compensate for assuming the credit risk. Such measure of credit quality should enable comparison between securities issued by a company and also between securities issued by other companies
YTM Assumptions:
- Investor can only achieve a return equal to the yield if the bond is held to maturity and if all coupons can be reinvested at the same rate
- Assumes yield curve is flat i.e. in practice we would expect different rates for different maturity. In YTM reinvestment rates are same for all maturities
Yield Spread: Difference between YTM of bond and the associated on the run (most recently issued) treasury with similar but not identical maturity
- It shares all the weaknesses of YTM in terms of reinvestment rate and hold to maturity
- Another disadvantage is that it is not a measure of return of a long bond
- It can only be used to compare different bonds with same maturity which may have different coupons
- Benchmark security is chosen to have maturity close to but not coincident with bond which means that measure is biased if the underlying benchmark is sloped
- Benchmark security can change over time as the bond rolls down the curve. Thus, it is not a consistent measure through time
Interpolated spread: I-Spread is the difference between YTM of the bond and interpolated yield to the same maturity on an appropriate reference curve
- Overcomes the issue of maturity mismatch but does not correspond to the YTM of a traded reference bond
- If the reference curve is upward sloping and the benchmark has a shorter maturity then I-spread will be less than the yield spread and vice versa
- Accounts for shape of the term structure in a crude way
Option Adjusted Spread (OAS): Parallel shift to the LIBOR zero rate curve required in order that the adjusted curve re-prices the bond
- Typically measured against LIBOR and was originally conceived as a measure of the amount of optionality priced into a callable and puttable bond
- Reflects a parallel shift of the spread against LIBOR thus takes shape of the term structure into account
- Assumes that cash-flow can be reinvested in LIBOR+OAS
- OAS is higher than I-spread when reference curve is upward sloping and is less when the curve is inverted. The magnitude depends on the compounding frequency
Asset Swap Spread (ASW): Spread paid over LIBOR on the floating leg in a par asset swap package
- It is a traded spread rather than an artificial measure
- 2 components:
  - At initiation investor pays par and receives the bond, which is worth its fill price
  - Investor enters into an interest rate swap paying fixed cash-flows that are identical in size and timing to the coupon of the bond. In return, the investor receives a fixed spread over LIBOR called ASW
- If the assets (bond) in ASW defaults then unwind cost is taken by the buyer. The loss is P-R i.e. difference between price paid and the recovery price
- Increase in bond price results in fall in the ASW as the implied credit risk of the issuer decreasing
Quoted Margin (QM): Spread over the LIBOR paid by floating rate note. Analogous to coupon for fixed rate bond
- Not a dynamic measure as it reflects the credit quality of the issuer on the issue date of the bond
Discounted Margin (DM): Fixed add-on to LIBOR that is required to re-price the bond. Analogous to YTM for fixed rate bond
- Assumes underlying reference curve is flat
- Measures yield relative to current LIBOR and does not take the term structure into account
- Assumes that all future realized LIBOR rates will be equal to current LIBOR rate
Zero Discount Margin (Z-DM): Parallel shift to the forward LIBOR curve that is required to re-price the FRN. Analogous to OAS or zero volatility spread (Z-Spread)
- Forward LIBOR rates are used to project the cash-flows and adjusted by Z-DM to calculate the discount rates
- For upward sloping yield curves, Z-DM is less than DM
Credit Default Swap Spread (CDS-spread): Premium paid to a protection seller in CDS contract. Analogous to ASW
- Measures compensation to an investor for taking on the risk of losing par minus the recovery rate of the bond
- Arguably the best measure of credit risk for several reasons:
  - Almost a pure credit play with low interest rate risk
  - Corresponds to realizable stream of cash-flows
  - Investor can trade CDS to a number of fixed terms so we should be able to observe a term structure
  - CDS market is relatively liquid

Risk Premium of Corporate Bonds

Credit Risk Premium is similar to equity risk premium

Defined as the non-default component of corporate bond spreads
To ensure proper comparison, credit risk premium should be adjusted for the difference between expected returns on T-Bonds and T-Bills
Non-monotonically related credit ratings

Although yield spreads of risky bonds over treasury are observable, it is hard to tell how much is the compensation for the expected default and how is due to risk aversion and other factors

2 classes of pricing models to estimate default rates requiring an assumption that credit risk premium is zero

Reduced Form Models
Mathematically, complex structural approach based on option pricing

Both models reach the same conclusion that spreads on corporate bonds are much wider than what would be required to compensate for credit losses alone

This difference is assumed to be credit risk premium

Illiquidity is often cited as a reason for positive non-default components of spreads
Estimating required compensation for illiquidity is not easy
Liquidity premium and credit risk premium are closely related

Credit risk premium rises as ratings deteriorate

Each type of model has its weakness

Structural model rely too much on equity market
In the transition model, variance is high and default rates fluctuate from long term average

BB rated bonds tend to outperform other credit tiers on a total return basis

Implies BB bonds have had the highest credit risk premium
From highest rated until BB more risky bonds outperform less risky ones on absolute basis
After BB the relationship is reversed
CCC rated bonds have had negative returns over treasury bonds. However, during recovery following a recession they perform quite strongly

Active investors can add value to their portfolio by tactically adding B and CCC rated bonds during market upswings and removing during downturn. Passive investors looking for highest returns should invest in BB as they have the best absolute performance

In risk adjusted returns (Sharpe Ratio) AAA, AA & A rated bonds are better

Given a relatively short history of B and CCC bonds, investors have underestimated their propensity to default and thus the realized risk premiums for these have been lower

There have been only 2 recessions for the B rated (1999 & 2001) and only 1 for CCC (2001)

3 reasons for why expected returns in BB and not B CCC have been higher

Lack of natural buyers for BB and fallen angel effect where investment grade bonds enter at attractive prices
High yield investors have overestimated their security selection skills. Search for yield leads them to B & CCC instead of BB
Investors may have bought lowest tiers anticipating a supportive environment

India's Top 10 Paymasters

I posted a comment to the post at Trak.In, which was in response to an article on Economic Times.

It is surprising that newspaper would publish something without citing their methodology. I doubt they would have surveyed employees to arrive at the figure.

I think they would have taken the salary expense from the annual / quarterly statements and divided it by the total number of employees in the company.

Average in this case may not even be close to what most people would actually earn as averages are influenced by outliers. Consider a company with 11 employees. The CEO earns 1 Cr p.a. and other 10 earn 10 Lac p.a. the average will be around 18 Lac p.a.

When data has outliers median may be a better indication of the actual salary most people would earn. The median in my example is 10 Lac p.a.

So it is interesting to see the methodology employed by ET if they have just used annual statements then there is no way they would have median salary (or standard deviation around the average). If they have done surveys then median would be a better estimate.