Actuarial Notes

Comprehensive Income

Study guide: Exam 6C

Comprehensive Income is the total change in an insurer's equity during a period from all sources other than transactions with shareholders. It is Net Income plus other comprehensive income (OCI) — items that IFRS requires or permits to be recognised outside profit or loss.

\text{Comprehensive income} = \text{Net income} + \text{OCI}

  • What sits in OCI for a P&C insurer:
    • Unrealised gains and losses on investments classified at fair value through OCI, which is where most Canadian insurers hold their bond portfolios.
    • The effect of changes in discount rates on insurance liabilities, where the OCI option has been elected.
    • Remeasurements of defined benefit pension plans, and currency translation on foreign operations.
  • Recycling. Some OCI items are later reclassified into profit or loss (realised gains on FVOCI debt instruments, and the accumulated insurance finance amounts as liabilities run off); others never are (pension remeasurements, FVOCI equity gains). Whether an item recycles determines whether it will ever affect reported earnings.
  • Why it matters for insurers specifically. OCI is where accounting mismatch is managed. Bonds at FVOCI move with rates; if the matching liability movement is also in OCI, the two offset there and profit is left showing underwriting and the predictable unwind. If they are split across statements, reported profit swings for no economic reason.
  • Accumulated OCI is part of equity, and therefore part of Capital Available and the MCT ratio. A sharp rise in interest rates reduces the value of FVOCI bonds, reduces accumulated OCI, and reduces the capital ratio — even though the insurer intends to hold the bonds to maturity and will suffer no loss.
  • Comprehensive income is the more complete measure of the period's economics; net income is the more closely watched. An analyst should read both, and read the gap between them as a measure of how much of the period's change in position was routed around the income statement.

A Rate Rise Through the Statements Interest rates rise 150 basis points during the year. An insurer holds \$900 million of FVOCI bonds with duration 4 years, and insurance liabilities of \$780 million with duration 3 years, for which it has elected the OCI option. Net income before these effects is \$50 million.

Compute net income and comprehensive income.

Answer Bond value falls:

\begin{align*}
\Delta A &\approx -4 \times 0.015 \times \$900\text{M} \\
&= -\$54\text{M}
\end{align*}

recognised in OCI.

Liability value falls (a gain to the insurer, since the liability is now worth less):

\begin{align*}
\Delta L &\approx -3 \times 0.015 \times \$780\text{M} \\
&= -\$35\text{M}
\end{align*}

and with the OCI option elected, this +\$35M gain also goes to OCI.

Results:

\begin{align*}
\text{Net income} &= \$50\text{M} \\[4pt]
\text{OCI} &= -\$54\text{M} + \$35\text{M} = -\$19\text{M} \\[4pt]
\text{Comprehensive income} &= \$50\text{M} - \$19\text{M} = \$31\text{M}
\end{align*}

What the -\$19 million represents. It is the duration mismatch: assets at 4 years against liabilities at 3 years, so a rate rise hurts the assets more than it helps the liabilities. That is a genuine economic loss, and it is exactly the figure a reader wants.

Two further observations. First, equity and hence Capital Available fall by \$19 million net, so the MCT ratio moves even though net income was untouched. Second, had the insurer not elected the OCI option, net income would have been \$50 + \$35 = \$85 million and OCI -\$54 million — the same comprehensive income, but a reported profit inflated 70\% by a rate movement. That contrast is the entire case for the option.