Class 3 — Bond Pricing, ALM, and Market Value Adjustment (MVA)¶

This session connects MYGA product mechanics to the asset side of the balance sheet. We begin with a refresh on bond cash flows and pricing, then extend those ideas to asset–liability management (ALM), spread-based earnings, and the economic logic behind Market Value Adjustment (MVA).

We conclude with a deeper look at annuitization options and what income conversion means in practice.

Big picture

You cannot understand MYGA products without understanding: - how assets are priced - how assets earn returns - and what happens when interest rates change

1. Bond Cash Flows (Refresher)¶

Fixed-income assets are the primary backing for MYGA liabilities. We start with a standard coupon bond.

1.1 Bond Cash Flow Structure¶

Consider a bond with: - Face value: $100 - Coupon rate: 4% annually - Coupon frequency: semiannual - Maturity: 5 years

Cash flows

At purchase (time 0): investor pays market price
Every 6 months: coupon payment
At maturity: final coupon + principal repayment

Bond cash flow timeline (semiannual)

Time:   0    0.5    1.0    1.5    2.0    ...    5.0
        |-----|------|------|------|------|------|
Cash:  -P     C      C      C      C      ...   C+100

Where: - $C = 100 \times 4\% / 2 = 2$

2. Bond Pricing and Market Value¶

2.1 Market Value of a Bond¶

The market value of a bond is the present value of its future cash flows, discounted at the current market yield.

\[ MV = \sum_{t=1}^{n} \frac{C_t}{(1+y)^t} \]

Where: - $C_t$ = cash flow at time $t$ - $y$ = market yield per period

Key point

Market value depends on current interest rates, not the coupon rate.

2.2 Par, Premium, and Discount Bonds¶

Price vs Par	Description
$MV = 100$	Bond trades at par
$MV > 100$	Bond trades at a premium
$MV < 100$	Bond trades at a discount

Economic intuition

Coupon > market yield → premium bond
Coupon < market yield → discount bond

At time 0: - buying a premium bond means paying more than face value - buying a discount bond means paying less than face value

2.3 Book Value vs Market Value¶

Concept	Meaning
Market value	Price if bond is sold today
Book value	Amortized cost on insurer’s books

For insurers: - assets are often held at book value - gains and losses are realized when assets are sold

Important distinction

Market value drives economic reality. Book value drives accounting presentation.

3. Interest Rate Sensitivity¶

3.1 Interest Rate Movements¶

When interest rates rise → bond prices fall
When interest rates fall → bond prices rise

This inverse relationship is fundamental to MVA design.

3.2 Duration (Conceptual)¶

Duration measures a bond’s sensitivity to interest rate changes.

What duration tells you

Approximate % change in price for a 1% change in yield.

Example: - Duration = 5 - Rates increase by 1% - Bond price decreases by ≈ 5%

We will focus on effective duration intuition, not formal derivations.

4. Asset–Liability Management (ALM) for MYGA¶

4.1 Asset Portfolio for MYGA¶

MYGA premiums are typically invested in fixed-income assets, such as:

corporate bonds
structured notes
mortgage-backed securities
commercial mortgage loans
select CLO tranches

Unifying idea

Regardless of asset type, the goal is the same: earn a predictable return to support guaranteed liabilities.

4.2 Net Earned Rate and Spread¶

Define:

Asset Earned Rate (AER): yield earned on assets
Credited Rate: interest credited to policyholders
Spread = AER – Credited Rate

Typical spread economics

Asset earned rate: 5.5%
MYGA credited rate: 4.0%
Spread: 1.5% (150 bps)

The spread is used to: - cover expenses - absorb risks - generate profit

Industry reality

Typical long-run spreads: - ~100–200 bps - renewal rates are often lower than initial rates - spreads generally widen after the guarantee period

5. Why Market Value Adjustment (MVA) Exists¶

5.1 The Economic Problem¶

Suppose: - Insurer purchased assets when rates were low - Interest rates rise - Policyholder surrenders early

To pay the surrender value: - insurer may need to sell assets - assets now have lower market value

This creates a market value loss.

Market Value Adjustment (MVA) passes part of the asset gain/loss to the policyholder.

Key principle

MVA aligns the liability payout with the economic value of assets.

5.3 Simple MVA Example¶

Assume: - Initial credited rate: 4% - Current market rate: 6% - Remaining duration: 3 years

Rates increased → asset value declined.

Simplified intuition: - higher current rates → negative MVA - lower current rates → positive MVA

Product design detail

Many MVAs are calculated using: - reference yields - spread offsets - duration-based formulas

Exact formulas vary by product.

6. Annuitization Options¶

Annuitization converts account value into a stream of income payments.

6.1 Common Annuitization Forms¶

Option	Description
Life only	Payments for life, stop at death
Life with period certain	Minimum guaranteed payment period
Period certain	Payments for fixed number of years
Joint life	Payments continue while either life is alive

6.2 Numerical Illustration¶

Assume: - Account value at annuitization: $100,000 - Life expectancy: 20 years (240 months) - Simplified payout factor

Life only (illustrative)

\[ \text{Monthly Payment} \approx \frac{100{,}000}{240} \approx 417 \]

Life with 15-year certain

Payments guaranteed for at least 180 months
Monthly payment slightly lower due to guarantee

Why this matters

Annuitization changes the insurer’s risk from: - accumulation risk - to longevity and payout risk

7. Key Takeaways¶

After this class, you should understand:

how bond cash flows and pricing work
the difference between market value and book value
why interest rate changes create gains and losses
how MYGA products earn spread through ALM
why MVA is economically necessary
how annuitization options reshape cash flows

8. Looking Ahead¶

Next class

In Class 4, we will shift from product economics to statutory reserving.

We will introduce:

CARVM (Commissioners Annuity Reserve Valuation Method)
Relevant NAIC guidance (including AG 33 and VM-22 context)
How CARVM translates product guarantees into reserves
Step-by-step reserve calculation intuition

This will complete the bridge from: product → assets → economics → statutory reserves.