Total returns on equities, bonds and cash; inflation

Introduction: Why Returns and Inflation Matter

Welcome to one of the most fundamental chapters in the Investment and asset-liability management section. As an actuary, you aren't just looking at how much money is in a pot today; you are looking at how that money grows over time to meet future liabilities. To do that, you need to understand Total Returns.

Think of total return as the "full story" of an investment. It’s not just the interest or dividends you receive in your hand; it’s also how much the investment itself has increased (or decreased!) in value. When we add the "villain" of the story—inflation—we start to see the difference between getting "more money" and being "wealthier."

In this chapter, we will break down the components of returns for the three main asset classes and explore how they dance to the tune of inflation.

1. The Concept of Total Return

Before looking at specific assets, let’s define the "Universal Formula" for return. Total return consists of two parts: Income and Capital Growth.

\( Total Return = \frac{Income + (Ending Value - Starting Value)}{Starting Value} \)

Quick Tip: In CP1, always remember that "return" usually refers to the nominal return unless the word "real" is used. Nominal is the face-value percentage; Real Return is what’s left after you subtract inflation.

2. Equities: The Growth Engine

Equities (shares in a company) are generally expected to provide higher returns than bonds or cash over the long term because they are riskier. Their total return has three main drivers:

A. Dividend Yield (The Income)

This is the cash paid out to shareholders. If a share costs \( \$100 \) and pays a \( \$3 \) dividend, the yield is \( 3\% \).

B. Growth in Earnings (The Engine)

Over the long term, a company's share price tends to follow its earnings. If a company becomes more profitable, its value usually rises. This is the primary source of Capital Growth.

C. Changes in Valuation (The P/E Ratio)

Sometimes the price goes up just because investors are "feeling good" about the future, even if earnings haven't changed yet. This is reflected in the Price-to-Earnings (P/E) ratio. If the P/E ratio expands, you get a boost in capital growth.

The Equity Relationship:
\( Total Return \approx Dividend Yield + Rate of Growth in Earnings \)

Real-world analogy: Imagine owning a coffee shop. Your "Dividend" is the profit you take home at the end of the month to spend. Your "Capital Growth" is the fact that the shop is now worth more because you bought a better espresso machine and have more customers.

3. Bonds: The Fixed Income

Bonds are essentially loans to a government or a company. Their returns are much more "locked in" than equities, but they still fluctuate.

A. The Coupon (The Income)

Most bonds pay a fixed interest rate (the coupon). Unlike dividends, these are usually legal obligations.

B. Price Changes (The Capital Growth/Loss)

The price of a bond moves inversely to market interest rates.

• If interest rates rise, existing bond prices fall (because new bonds pay more).
• If interest rates fall, existing bond prices rise.

Key Takeaway: For a bond held to maturity, the total return is the Gross Redemption Yield (GRY). If you sell it early, your return will depend on how market yields have moved since you bought it.

4. Cash: The Safe Haven?

Cash (including short-term money market instruments) is unique because its Capital Value is generally stable (nominal value doesn't change), but its Income varies.

Components:
The total return on cash is almost entirely composed of Interest. There is virtually no capital growth in nominal terms.

The Catch: While cash is "safe" because you won't lose your nominal dollars, it is risky in terms of Inflation. If inflation is \( 5\% \) and your cash earns \( 2\% \), you are actually losing purchasing power.

5. Understanding Inflation

Actuaries care deeply about inflation because many benefits payable on contingent events (like pensions) are linked to it.

Price Inflation

This measures the change in the cost of a "basket" of goods and services (e.g., bread, rent, fuel). This is what we usually mean when we say "inflation."

Earnings Inflation

This measures the change in average wages. Historically, earnings inflation tends to be higher than price inflation. Why? Because of productivity gains. As workers become more efficient, they can be paid more than just the increase in the cost of living.

Key Formula (The Fisher Equation):
To find the Real Rate of Return (\( r \)), we use the nominal rate (\( i \)) and the inflation rate (\( e \)):
\( (1 + i) = (1 + r)(1 + e) \)

Simple Approximation: \( r \approx i - e \)

6. Theoretical Relationships: Putting it All Together

The syllabus requires you to understand how these returns relate to each other and to inflation. Here is the hierarchy you should keep in mind:

The Risk Premium

Investors demand a higher return for taking on more risk. This leads to the following theoretical relationship in expected returns:
Expected Return on Equities > Expected Return on Bonds > Expected Return on Cash

The Relationship with Inflation

1. Equities and Inflation: Equities are often seen as a "real" asset. Companies can raise their prices when inflation hits, which increases earnings and, eventually, dividends. Therefore, equity returns should, in the long run, exceed inflation.

2. Bonds and Inflation:

• Fixed-interest bonds are "inflation's victims." If inflation rises, the fixed coupon becomes worth less in real terms.
• Index-linked bonds are designed to protect against this, as their coupons and principal increase in line with a price index.

3. Cash and Inflation: Central banks often raise interest rates to fight inflation. While cash returns usually move in the same direction as inflation, they may lag behind during periods of very rapid price increases.

Summary Checklist

✓ Equities: Return = Dividends + Earnings Growth + P/E change. Linked to real economic growth.

✓ Bonds: Return = Coupons + Price changes (due to yield shifts). Vulnerable to inflation unless index-linked.

✓ Cash: Return = Interest. Low nominal risk, high real risk.

✓ Inflation: Earnings inflation > Price inflation (usually) due to productivity.

✓ Real Returns: Always use \( (1+i) = (1+r)(1+e) \) to switch between nominal and real worlds.

Don't worry if the link between bond yields and prices feels counter-intuitive at first. Just remember: if "new" bonds are paying better interest, "old" bonds with lower interest become less attractive, so their price must drop!

Next Step: Now that you understand the components of returns, you can look at the Valuation of individual investments to see how we put a price tag on these expected future returns.