5.3 Equity, Fixed Income, Duration, and Alternative Assets

Equity, Fixed Income, Duration, and Alternative Assets

Quick Answer: Fixed income valuation centers on the inverse relationship between price and yield, measured by Modified Duration (price sensitivity) and Convexity (curvature). Fiduciaries must evaluate callable debt using Yield to Worst (YTW) and municipal debt using Taxable Equivalent Yield (TEY). Equity valuation employs the Gordon Growth Model ($P_0 = D_1 / (r - g)$) and valuation multiples. Alternative assets (REITs, Private Equity, Hedge Funds) are permitted under UPIA § 2(e) to enhance diversification, provided the trustee prudently manages illiquidity, capital call commitments, and fee structures.

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1. Fixed Income Mechanics & Yield Relationships

Bonds represent contractual debt obligations. Fiduciaries must understand how bond yields interact across par, premium, and discount pricing.

┌─────────────────────────────────────────────────────────────────────────────┐
│                     BOND PRICING & YIELD RELATIONSHIPS                      │
├──────────────────┬──────────────────────────────────────────────────────────┤
│ Pricing Status   │ Yield Hierarchy (Lowest to Highest)                      │
├──────────────────┼──────────────────────────────────────────────────────────┤
│ **Discount**     │ Coupon Rate < Current Yield < Yield to Maturity (YTM)    │
│ (Price < Par)    │ < Yield to Call (YTC)                                    │
├──────────────────┼──────────────────────────────────────────────────────────┤
│ **Par Value**    │ Coupon Rate = Current Yield = Yield to Maturity = YTC    │
│ (Price = Par)    │                                                          │
├──────────────────┼──────────────────────────────────────────────────────────┤
│ **Premium**      │ Yield to Call (YTC) < Yield to Maturity (YTM)            │
│ (Price > Par)    │ < Current Yield < Coupon Rate                            │
└──────────────────┴──────────────────────────────────────────────────────────┘

Key Yield Definitions

1. Nominal Yield (Coupon Rate): Fixed annual dollar interest paid divided by par value ($1,000).
2. Current Yield: Annual dollar coupon divided by the current market price: $\text{Current Yield} = \frac{\text{Annual Dollar Coupon}}{\text{Current Market Price}}$
3. Yield to Maturity (YTM): The internal rate of return (IRR) earned on a bond held to maturity, assuming all interim coupon payments are reinvested at the YTM rate.
4. Yield to Call (YTC): The internal rate of return earned if a callable bond is called by the issuer at the earliest call date at the call price.
5. Yield to Worst (YTW) Fiduciary Mandate: For callable bonds trading at a premium, the issuer has an economic incentive to refinance; therefore, YTC is lower than YTM. A fiduciary must always quote and evaluate callable premium bonds on Yield to Call / Yield to Worst to avoid overstating expected portfolio income.

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2. Yield Curve Shapes & Economic Theories

The yield curve graphs the yields of bonds of identical credit quality (typically U.S. Treasuries) across maturities from 1 month to 30 years.

Yield (%)
  ▲       NORMAL (Upward)           INVERTED (Downward)         FLAT / HUMPED
  │           .---'                     '---.                      .----.
  │        .-'                               '-.                .-'      '-.
  │     .-'       Economic                  .-'  Precursor to  '------------'
  │  .-'          Expansion              .-'     Recession     Transition Phase
  └──────────────────────► Maturity ───────────────────► Maturity ──────────►

1. Normal (Upward Sloping): Longer maturities offer higher yields to compensate investors for interest rate risk and inflation uncertainty over time. Reflects healthy economic growth.
2. Inverted (Downward Sloping): Short-term yields exceed long-term yields. Occurs when central banks aggressively hike short-term rates to fight inflation while markets anticipate future economic slowdown and rate cuts. Historically the most reliable leading indicator of a macroeconomic recession.
3. Flat: Short-term and long-term yields are virtually identical. Indicates an economic inflection point or transition between expansion and contraction.
4. Humped: Intermediate-term yields are higher than both short-term and long-term yields. Reflects near-term monetary policy uncertainty.

Yield Curve Theories

• Pure Expectations Theory: Long-term rates reflect market expectations of future short-term rates.
• Liquidity Preference Theory: Investors require a positive liquidity premium (term premium) to hold longer-term debt due to greater price volatility.
• Market Segmentation / Preferred Habitat Theory: Yields at each maturity are determined independently by supply and demand dynamics from specific institutional participants (e.g., commercial banks in short-term paper, pension funds in 30-year debt).

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3. Interest Rate Risk: Duration and Convexity

Bond prices move inversely to interest rates. However, price sensitivity varies drastically based on coupon rate, maturity, and yield level.

Macaulay Duration

Macaulay Duration is the weighted-average time (measured in years) until a bond's cash flows (coupons and principal) are received:

• For a zero-coupon bond, Macaulay Duration equals its maturity.
• For a coupon-bearing bond, Macaulay Duration is always less than its stated maturity.
• Lower coupon rates and longer maturities increase duration.

Modified Duration & Price Sensitivity

Modified Duration measures the percentage change in a bond's price for a 100 basis point (1.0%) change in yield:

$\text{Modified Duration} = \frac{\text{Macaulay Duration}}{1 + \left(\frac{y}{k}\right)}$

Where $y$ is the Yield to Maturity and $k$ is the compounding frequency per year (e.g., $k=2$ for semiannual).

$\%\Delta P \approx -\text{Modified Duration} \times \Delta y$

Worked Duration Calculation

A corporate trustee holds a $5,000,000 bond portfolio with a Modified Duration of 6.50 years. If market interest rates rise by 75 basis points (+0.75%):

$\%\Delta P \approx -6.50 \times (+0.0075) = -4.875\%$ $\text{Dollar Loss} = \$5,000,000 \times (-0.04875) = -\$243,750$

Convexity

Because the price-yield relationship is a curved (convex) line rather than a straight tangent line, Modified Duration is only an approximation. Convexity measures the rate of change of duration as yields change:

• Positive Convexity (Standard Option-Free Bonds): When interest rates fall, bond prices increase at an accelerating rate; when rates rise, bond prices fall at a decelerating rate. Positive convexity is highly advantageous to bondholders.
• Negative Convexity (Callable Bonds & Mortgage-Backed Securities / MBS): As interest rates fall, mortgage prepayments accelerate (refinancing), capping upside price appreciation (contraction risk). As interest rates rise, prepayments halt, lengthening the duration right when prices are falling (extension risk).

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4. Municipal Bonds in Fiduciary Portfolios

Interest on debt issued by state and local governments is exempt from federal income taxation under IRC § 103.

Taxable Equivalent Yield (TEY)

To compare a tax-exempt municipal bond yield to a fully taxable corporate or Treasury bond yield, fiduciaries calculate the Taxable Equivalent Yield (TEY):

$\text{TEY} = \frac{\text{Municipal Tax-Exempt Yield}}{1 - t_{\text{marginal}}}$

Where $t_{\text{marginal}}$ is the client's or trust's marginal federal income tax rate (plus the 3.8% Net Investment Income Tax if applicable).

Worked Fiduciary TEY Example

An irrevocable non-grantor trust in the top federal bracket ($37% + 3.8% \text{ NIIT} = 40.8%$) evaluates a high-grade municipal bond yielding $3.50%$ versus a corporate bond yielding $5.50%$:

$\text{TEY} = \frac{3.50\%}{1 - 0.408} = \frac{3.50\%}{0.592} = 5.912\%$

Fiduciary Conclusion: The municipal bond's Taxable Equivalent Yield of $5.91%$ exceeds the taxable corporate bond's yield of $5.50%$. The municipal bond delivers higher after-tax cash income to the trust.

Private Activity Bonds and the AMT

Certain municipal revenue bonds (e.g., stadium financing, industrial development, private airport facilities) are classified as Private Activity Bonds. While exempt from regular federal income tax, interest on non-essential private activity bonds is a tax preference item under IRC § 57(a)(5) and is subject to the Alternative Minimum Tax (AMT). Fiduciaries must screen beneficiary tax profiles prior to purchasing private activity municipal debt.

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5. Equity Valuation & Style Box Analysis

┌─────────────────────────────────────────────────────────────────────────────┐
│                     THE MORNINGSTAR EQUITY STYLE BOX                        │
├──────────────────┬──────────────────┬──────────────────┬────────────────────┤
│ Market Cap       │ VALUE            │ BLEND            │ GROWTH             │
├──────────────────┼──────────────────┼──────────────────┼────────────────────┤
│ **Large-Cap**    │ Low P/E, High Div│ Core Indexing    │ High P/E, High EPS │
│ (> $10B)         │ Financials, Energy (S&P 500)        │ Tech, Cons Discret │
├──────────────────┼──────────────────┼──────────────────┼────────────────────┤
│ **Mid-Cap**      │ Industrial Value │ Broad Mid-Market │ Expanding Mid-Cap  │
│ ($2B - $10B)     │ Cyclical Leaders │ (Russell Midcap) │ Tech Innovators    │
├──────────────────┼──────────────────┼──────────────────┼────────────────────┤
│ **Small-Cap**    │ Regional Banks   │ Small Core       │ Emerging Biotech,  │
│ (< $2B)          │ Distressed Value │ (Russell 2000)   │ Software Pureplays │
└──────────────────┴──────────────────┴──────────────────┴────────────────────┘

Fundamental Equity Valuation: The Dividend Discount Model (DDM)

The Gordon Growth Model calculates the intrinsic value of a dividend-paying stock assuming constant dividend growth:

$P_0 = \frac{D_1}{r - g} = \frac{D_0 (1 + g)}{r - g}$

Where:

• $P_0$ = Intrinsic value of the stock today
• $D_1$ = Expected dividend next year ($D_0 \times (1 + g)$)
• $r$ = Required rate of return (from CAPM)
• $g$ = Constant perpetual dividend growth rate (where $r > g$)

Worked Gordon Growth Example

A stock just paid an annual dividend of $D_0 = $2.50$. Dividends are projected to grow at a constant rate of $g = 5.0%$ annually. The required rate of return is $r = 9.0%$:

1. Calculate next year's dividend: $D_1 = $2.50 \times (1 + 0.05) = $2.625$
2. Calculate intrinsic value: $P_0 = \frac{$2.625}{0.09 - 0.05} = \frac{$2.625}{0.04} = $65.625$

If the stock is currently trading at $58.00 in the market, it is undervalued and represents an attractive purchase.

Key Valuation Multiples

• Price-to-Earnings (P/E): Compares share price to earnings per share. Trailing P/E uses past 12 months; Forward P/E uses next 12 months projected EPS. The PEG Ratio divides P/E by annual EPS growth rate (PEG < 1.0 suggests undervaluation relative to growth).
• Price-to-Book (P/B): Compares market value to accounting book value. Useful for capital-intensive firms and financial institutions.
• EV/EBITDA: Enterprise Value divided by Earnings Before Interest, Taxes, Depreciation, and Amortization. Capital-structure-neutral valuation metric.

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6. Alternative Assets in Fiduciary Portfolios

Under UPIA § 2(e), no category of asset is per se prohibited. Trustees may include alternative asset classes to harvest the illiquidity premium and achieve non-correlated return streams:

┌─────────────────────────────────────────────────────────────────────────────┐
│                     ALTERNATIVE ASSET CLASS CHARACTERISTICS                 │
├──────────────┬──────────────────┬────────────────────┬──────────────────────┤
│ Asset Class  │ Primary Role     │ Key Fiduciary Risk │ Liquidity / Term     │
├──────────────┼──────────────────┼────────────────────┼──────────────────────┤
│ **REITs**    │ Real estate cash │ Interest rate risk │ Daily liquidity      │
│              │ yield & inflation│ & economic cycles  │ (Publicly traded)    │
├──────────────┼──────────────────┼────────────────────┼──────────────────────┤
│ **Private**  │ Superior capital │ Extreme illiquidity│ 7–12 Year Lockup     │
│ **Equity**   │ appreciation     │ & J-Curve drawdowns│ (Capital calls)      │
├──────────────┼──────────────────┼────────────────────┼──────────────────────┤
│ **Hedge**    │ Downside hedge & │ High fee structure │ Quarterly/Annual     │
│ **Funds**    │ non-correlated α │ & gate restrictions│ (Lockups & Gates)    │
├──────────────┼──────────────────┼────────────────────┼──────────────────────┤
│ **Commod-**  │ Direct inflation │ High volatility &  │ Daily liquidity      │
│ **ities**    │ hedge / input cost│ negative roll yield│ (Futures / ETFs)     │
└──────────────┴──────────────────┴────────────────────┴──────────────────────┘

Real Estate Investment Trusts (REITs)

• Must distribute at least 90% of taxable income to shareholders annually to maintain pass-through tax status.
• Dividends are taxed as ordinary income (not qualified dividends), making REITs highly tax-inefficient inside non-grantor taxable trusts. Best located in tax-deferred or tax-exempt accounts.

Private Equity (PE) & The J-Curve

• Structure: 10-year limited partnerships. Investors make capital commitments, drawn down via capital calls during the first 3 to 5 years (investment period).
• The J-Curve Effect: In early years, net returns are negative due to upfront management fees, transaction costs, and un-realized investments. Substantial positive cash returns occur in years 5–10 as portfolio companies are harvested and liquidated.
• Fiduciary Prudence: A trustee must ensure the trust maintains sufficient liquid cash reserves to satisfy mandatory capital calls without triggering emergency liquidations of other assets.

Hedge Funds

• Strategies include Long/Short Equity, Global Macro, Market Neutral, and Event-Driven/Distressed Debt.
• Fee structures historically "2 and 20" (2% management fee plus 20% incentive fee over a hurdle rate with a high-water mark).
• Impose redemption restrictions: lock-up periods (1–3 years) and gates (limiting quarterly fund withdrawals to 10–25% of total fund assets during crises).

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7. Real Estate, Farmland, Unique Assets, and Digital Assets

Beyond liquid securities, fiduciary accounts regularly hold directly owned real property and specialty assets that the blueprint lists as their own asset-type topic:

• Direct Real Estate: provides income plus appreciation with low correlation to public equities, but imposes fiduciary burdens — periodic revaluation for accountings, environmental diligence (CERCLA Phase I site assessments before acceptance), leasing and insurance titling, and liability management.
• Farmland and Timberland: generate crop-share or lease income plus land appreciation; fiduciary issues include conservation easements, multi-generational succession, and commodity-cycle valuation swings. Farmland has historically served as an inflation-sensitive real-asset diversifier in trust portfolios.
• Unique / Hard-to-Value Assets: oil, gas, and mineral interests divide into royalty interests (pure revenue share without expense or liability) and working interests (revenue share minus joint-operating expenses and operator-liability exposure), with depletion deductions sheltering part of the income; collectibles (art, coins, wine) produce no current income, are subject for individuals to a maximum 28% long-term capital-gains rate, and demand specialist appraisal, storage, and insurance.
• Digital Assets: cryptocurrencies, NFTs, domain names, monetized social-media accounts, email, photographs, and cloud documents. Two fiduciary disciplines apply: (1) custody and valuation — private-key or qualified-custodian control, wallet and exchange verification, and extreme volatility that must be documented in the IPS; and (2) fiduciary access — the Revised Uniform Fiduciary Access to Digital Assets Act (RUFADAA) establishes a three-tier access priority (the provider's online tool directive controls over the estate-planning document, which controls over the platform's terms of service) for trustees, executors, and agents. A prudent digital-asset inventory belongs in every estate plan and every pre-acceptance review.