Asset Allocation

Problem first. Many investors pick funds, sectors, or hot managers. They then wonder why outcomes diverge widely. A concrete example clarifies the failure. Two investors start with $100,000 each. Investor A uses a 60% stocks / 40% bonds split. Investor B uses an 80% stocks / 20% bonds split. If expected real returns are 5-7% for stocks and 0-2% for bonds, then A's weighted expected real return is about 3-5% and B's is about 4-6%. That difference of roughly 1 percentage point translates into a 35-50% difference in portfolio value over 30 years because of compounding at 1% extra per year. Volatility differences are larger. If stocks have annual volatility of 15-20% and bonds 3-6%, then A's portfolio volatility might be 9-11% while B's could be 12-15%, given a correlation range of 0.1-0.4. Those volatility ranges drive drawdown size and retiree outcomes. People often chase past winners or buy a single flashy ETF. The consequence is concentrated risk and variable returns that come from allocation, not security selection. This repeats a finding from the prerequisites. In Diversification we saw correlation effects. In Index Funds we saw why owning broad market exposures often beats active picks after fees. Missing the allocation step therefore leaves most of the portfolio's fate to chance. IF an investor changes the stock/bond split by 20 percentage points AND expected returns differ by 1 percentage point, THEN long-run wealth may diverge by 30-50% BECAUSE of compound growth and higher volatility compounding losses during bad years. Practical implication: allocation is the lever with the largest predictable impact. The remainder of this lesson explains the math, trade-offs, and decision rules that make allocation a repeatable, measurable choice.

Start with the mechanics. Asset Allocation is the weight vector that combines assets to form expected return and risk. For a two-asset mix of stocks (weight $w_s$) and bonds (weight $w_b = 1 - w_s$), expected portfolio return is

$E[R_p] = w_s E[R_s] + w_b E[R_b]$

If $E[R_s]$ is 5-7% real and $E[R_b]$ is 0-2% real, then a 70% equity weight gives $E[R_p]$ around 3.5-5.1% real. Variance follows

$\sigma_p^2 = w_s^2 \sigma_s^2 + w_b^2 \sigma_b^2 + 2 w_s w_b \sigma_s \sigma_b \rho_{s,b}$

where $\sigma_s$ and $\sigma_b$ are standard deviations and $\rho_{s,b}$ is correlation. Plug numbers. Let $\sigma_s = 16\%$, $\sigma_b = 5\%$, and $\rho = 0.2$. For $w_s = 0.60$ we get

$\sigma_p^2 = 0.36(0.16^2) + 0.16(0.05^2) + 2(0.6)(0.4)(0.16)(0.05)(0.2) \approx 0.0106$ so $\sigma_p \approx 10.3\%$.

For $w_s = 0.80$ the math gives $\sigma_p \approx 12.9\%$. That math shows how 20 percentage points in stock weight raise volatility by about 2.6 percentage points in this numeric example. Volatility maps to drawdowns. Historical equity drawdowns are often 30-50% over multi-year windows while bond drawdowns are typically 5-15% in stress. Sequence-of-returns risk matters when withdrawals start. Consider a retiree withdrawing 4% annually. Missing the bad sequence can reduce a 30-year success probability from, say, 85% to 50% depending on allocation and withdrawal size. That is why glide paths exist. A glide path is a schedule that reduces equity weight as the target date approaches. Targeted equations are simple. If equities start at $w_{s,0}$ at 30 years to retirement and decline linearly to $w_{s,R}$ at retirement, then $w_s(t) = w_{s,0} - \frac{w_{s,0} - w_{s,R}}{T} t$ where $T$ is years until retirement. IF an investor wants lower volatility AND has a 15-25 year horizon, THEN lowering equity weight by 10-20 percentage points may reduce volatility by about 1.5-3 percentage points BECAUSE bonds have lower volatility and negative or low correlation with stocks. The formulas above quantify trade-offs so choices are not guesswork but math.

What to do practically. Frame the decision as trade-offs, not commandments. Start with three inputs: time horizon in years, tolerance for drawdowns expressed as maximum expected peak-to-trough loss in percent, and liquidity needs measured in months of expenses. Use these numeric inputs to pick allocation bands. A compact rule set follows.

Age-based rules. Consider three variants with ranges based on historical risk-return patterns. Variant A uses the conservative rule of $\text{Stocks} = 100 - \text{age}$ giving stocks of 70% at age 30 and 40% at age 60. Variant B uses a modern higher-equity rule of $\text{Stocks} = 110 - \text{age}$ giving stocks of 80% at age 30 and 50% at age 60. Variant C uses $\text{Stocks} = 120 - \text{age}$ for long-horizon, high-return-seeking investors yielding 90% at 30 and 60% at 60. IF an investor has 30+ years until retirement AND is comfortable with a 12-18% annual volatility range, THEN a high-equity band of 70-90% equities may increase expected returns by 1-2 percentage points annually BECAUSE equities historically outperformed bonds by 3-5 percentage points before inflation over long windows.

Risk tolerance and glide paths. If the investor has low tolerance for a 30-50% drawdown, then a glide path to reach 30-40% equities at retirement may reduce sequence risk by 20-40% probability of failure for a given withdrawal rate. Target-date funds implement glide paths by design. Many Target-date funds start with 80-90% equities at 25-30 years to retirement and reach 30-40% equities at retirement; look for funds with explicit equity glide range of at least 40-60 percentage points.

Tax and liability overlays. IF high current taxable income exceeds $200,000 AND taxable bonds are used, THEN shifting tax-inefficient bonds into tax-deferred accounts may improve after-tax income by 0.3-1.0% annually BECAUSE municipal or tax-deferred wrappers reduce tax drag. Practical decision: use the age/horizon bands to set a default allocation, then adjust within +/- 10-15 percentage points for explicit liabilities, taxable status, or human tolerance. Target-date funds are a credible default if one wants a near-turnkey solution with a glide path and automatic rebalancing, but accept fees in the 0.10-0.75% range and check the underlying equity exposures.

Models break. Here are at least four specific scenarios where simple allocation advice fails. 1) Large concentrated stock positions. If a single employer stock represents more than 20-30% of investible assets, then portfolio-level risk is dominated by that concentration. The two-asset formulas above do not capture idiosyncratic single-name risk and tail risk that can exceed 50% loss in one event. IF concentrated stock exposure exists AND job income is correlated with that stock, THEN selling or hedging may materially reduce total household risk BECAUSE reducing correlation lowers combined volatility and downside exposure. 2) Near-retirement sequence-of-returns risk. For someone within 0-5 years of retirement withdrawing 4-6% annually, allocation swaps of 10-20 percentage points can change retirement success probabilities by 10-30 percentage points. Simple age rules understate this effect. 3) Illiquid or alternative allocations. Private equity, direct real estate, and venture exposures often report return ranges of 8-15% but have liquidity constraints and valuation lag. The two-asset variance formulas assume mark-to-market and continuous rebalancing; they break when assets cannot be rebalanced yearly. 4) Taxes and account location. A 1% fee or tax drag reduces compound wealth by roughly 10-20% over 30 years depending on pre-tax returns. The allocation framework here does not produce an optimal tax wrapper choice. It also omits behavioral factors. IF an investor cannot tolerate a 30-50% peak-to-trough loss without selling AND has a 30-year horizon, THEN a lower equity allocation may raise the probability of staying invested BECAUSE fewer and smaller losses reduce impulse selling during bad markets. Last, model calibration depends on input ranges. Expected returns of 5-7% for equities and 0-2% for bonds are plausible ranges; shifting those by 1-2 percentage points changes optimal allocation materially. Documenting assumptions and re-running scenarios with +/- 1-2% changes helps identify robustness limits.

Builds on prerequisites: Diversification (/money/123) for correlation and breadth effects, and Index Funds (/money/456) for choosing low-cost broad exposures. Understanding allocation unlocks Retirement Withdrawal Strategies (/money/789) because withdrawal success probabilities depend on allocation, and Tax-Efficient Investing (/money/321) because allocation decisions interact with account location and tax drag.