# 3.3 Index Construction

### Index Calculations

The main indices are weighted by market value. Alternative weighting schemes are also available on the EDHEC*infra* platform.

The total return is calculated by adding the income or cash yield, reflecting the debt service due to paid and accrued interest, and the price return, reflecting the gains or losses due to changes in the end-of-quarter price and principal repayments.

The **cash yield** represents the sum of interest payments and principal repayments:

where,

is cash yield at time t

is the interest payment at time t

is the principal repaid at time t

is the outstanding principal at time t-1

**Price** **Returns** are computed thus:

where,

is the bond price at time t

is the price return at time t

In addition, **yield-to-maturity** or internal rate of return equating the security’s price to its future cash flows is estimated as a solution of:

where,

is the bond price at time t

is the *i*th cash flow at time t

is the yield to maturity at time t

is the number of years until maturity at time t

The **duration** of each security is also computed as the standard Duration calculation, the time-weighted discounted value of future cash flows divided by the sum of discounted future cash flows.

where,

is the duration of the debt instrument at time t

is the number of years from time t

is the *i*th risk-free rate at time t

is the spread

is the number of years until maturity at time t

is the *i*th cash flow at time t

is the yield to maturity at time t

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