IGNITE EXTENDED / LESSON 22
Which risks should affect a required return?
A risk-classification and discount-rate rationale.
An expected return combines possible outcomes using their probabilities. It can be an outcome that never occurs in any individual scenario. The probability distribution matters because two investments can have the same mean and very different variation or downside exposure.
Specify the states, their probabilities and the return convention. A forecast based on historical averages also requires an argument for why those observations are informative about the future. The source chapter’s historical market charts describe their stated periods and are used here to explain risk measurement.
An investment’s contribution to portfolio risk depends on how its outcomes move with the other investments. Imperfectly related exposures can partly offset one another. The source’s portfolio diagrams explain why combining assets can reduce variation without eliminating every source of risk.
Company-specific events may diversify across a sufficiently broad portfolio. Common shocks can affect many holdings together. The benefit therefore depends on the weights, variances and covariances, rather than simply the count of investments. Correlations can also change across conditions.
Illustrative: 50% chance of +20% and 50% chance of −10% gives expected return +5%.
Expected return is a probability-weighted average. Risk concerns the possible deviations and their consequences. The average alone cannot describe the experience of holding the investment.
A probability-weighted average of possible returns.
The distribution and relevant consequences of outcomes. The average alone does not describe them.
Illustrative application: one investment returns 10% with certainty in a toy model. Another has equally likely returns of −20% and 40%, also averaging 10%. A person unable to absorb the loss faces a materially different decision despite the equal mean.
Examine outcomes and their co-movement with the rest of the portfolio, using the stated probabilities as assumptions rather than observations.
Total volatility describes variation in an investment’s own return. Beta describes sensitivity to the chosen market return in the model. A volatile asset can have modest beta if much of its variation is unrelated to that market.
The capital asset pricing model relates required return to a risk-free rate, beta and a market risk premium. It is a model with assumptions, not a direct price quote for every private venture. Illiquidity, financing constraints and concentrated exposure complicate its application to early businesses.
A diversified fund and a founder can evaluate the same venture while facing different personal consequences. The founder may have employment, wealth and years of effort tied to it. The fund can evaluate the venture as one exposure within a portfolio.
Separate the project’s possible cash outcomes from the decision maker’s risk capacity and preferences. A financing structure can redistribute outcomes without making the operating uncertainty disappear. This distinction connects the risk lesson to investor incentives and the economics of financing terms.
Idiosyncratic risk concerns events particular to an investment. Systematic risk concerns exposure to shared market movements. Diversification affects them differently.
Risk associated with broad market movements that remains relevant to a diversified investor.
Risk specific to an exposure that may be reduced through diversification.
Illustrative application: a single plant outage may be specific to one company. A broad decline in demand can affect many holdings together. Adding many similar businesses may therefore leave substantial shared exposure even when company-specific events average out more.
A founder concentrated in one company can experience risks that a diversified investor does not price in the same way.
These are teaching assumptions, not current rates or a ready-made startup discount rate.
Explains that investors can diversify more cheaply than firms, so diversification adds no value at the firm level (PV(AB) = PV(A) + PV(B)); the summary reports historical averages of about 4.0% a year for US Treasury bills and 11.1% for common stocks over 109 years, a 7.1% premium, and market standard deviation of about 15% to 20%.
Two benchmarks follow: discount safe projects at the risk-free rate and average-risk projects at the market's expected return. A venture like Relay sits outside both, which is why the rate needs an argument. The historical figures describe the chapter's sample period, not today's inputs.
Selected reading: PDF pages 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
The chapter develops measures of uncertain returns and explains diversification through the co-movement of holdings. An investment’s contribution to a portfolio depends on more than its own variability.
An expected return summarizes possible outcomes and probabilities. Variance and standard deviation describe dispersion around that expectation.
The chapter compares long-run asset returns and risk premiums. Those observations have sampling uncertainty and do not directly establish future expected returns.
Combining holdings can reduce exposure to company-specific outcomes. Shared market movements limit the risk that adding similar holdings can remove.
Beta measures sensitivity to the market in the stated model and estimation period. It differs from the total standard deviation of an individual holding.
Selected reading: PDF pages 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
Equal expected returns can accompany very different possible losses. The mean does not describe the range of outcomes a holder must be able to bear.
A large number of holdings can still move together. Examine relationships among returns, not only the count of investments.
A diversified investor and a founder concentrated in one venture face different total exposures. Distinguish the portfolio model from the person’s complete financial situation.
An investor who commits $1 today expects on average $1 x (1 + r)^t at time t, and the slide asks what the required rate r should be.
The rate is set by the investor's alternatives, not by the project. Relay's 20% or 30% hurdle is a claim about what capital of similar risk and illiquidity earns elsewhere.
Builds the required rate from US Treasury yields, a risk premium for non-diversifiable (systematic) risk measured as beta times the market risk premium, and a liquidity premium for assets that cannot be sold quickly without a discount.
Idiosyncratic risk earns no premium in this framework because diversified investors can remove it. That is the reason Relay's company-specific risks (ClinicOS revoking API access, uptake) belong in the cash-flow scenarios rather than in an inflated rate.
A road from LPs' required return (risk-free, beta, liquidity premium) to their target net multiple, the VC's gross multiple after fees and carry, the outsized return each deal must be able to produce because failure rates are high, the VC's ownership at exit, and the valuation offered today.
This chain explains why VC hurdle rates look far above CAPM: they are applied to success-case projections and must cover failures, fees and illiquidity. It connects this lesson's rate to the VC-method valuation in lesson 31.
The finance materials distinguish investor required returns and portfolio economics from the venture’s operating uncertainties. A customer, execution or funding risk needs an operational response; labeling it “beta” does not produce a reliable valuation.
Which risks can this investor diversify, and which still affect the decision?
Damodaran's data page lists a US Treasury rate of 5.29% as the dollar risk-free rate and an implied US equity risk premium of 4.20% as of October 1, 2026, with alternative estimates from 3.30% to 5.67%. The textbook's 3% risk-free illustration understates today's base.
A CAPM benchmark built with these inputs (about 10.3% at beta 1.2) is a floor for a diversified investor, not a venture rate. Record the source and date of each input in the model so the rate can be updated rather than inherited.
Sources: Aswath Damodaran, NYU Stern: home page with current implied ERP · BVWire: Damodaran posts his first data update for 2026
Fictional venture risks: one key engineer may leave; a recession could reduce demand across customers; inventory can expire; the investor may need cash before an exit.
Classify the mechanisms. Explain which are operational, market-related or liquidity-related and why one arbitrary extra discount rate is not a complete response.
The second-EHR integration ($300,000 now; $150,000 of incremental gross profit a year for three years) has NPV +$15.97k at 20% and -$27.58k at 30%. Daniel argues for 20%; the seed lead, used to venture hurdle rates, argues for 30%. Relay's specific risks include ClinicOS-style API access terms at the second EHR, clinic uptake, and a two-person engineering team that would be fully committed for months.
Write a one-page rate rationale: classify Relay's risks, say which belong in the cash flows and which in the rate, state the rate and the cash-flow case it applies to, and show why the decision flips between 20% and 30%.
Haircutting cash flows for API loss and slow uptake and then also discounting at a venture rate built to cover those risks understates value. Pair expected cash flows with an expected-return rate, or plan-case flows with a hurdle rate, not both.
Beta measures sensitivity to market returns. A startup's chance of failing is mainly specific risk and belongs in the cash-flow scenarios.
A diversified fund prices systematic risk; a founder with most of their wealth and career in Relay bears total risk. Disagreements about Relay's risk can reflect different positions, not different forecasts.
A rate rationale for Relay: risks classified by type, a CAPM benchmark of about 10.3%, a defended choice between expected flows at 20% and plan flows at 30%, and the conclusion that uptake should be tested before committing $300,000.
Next lesson: Real options & staged commitments
Check your understanding
Question 1
Using a 5.29% Treasury rate, a 4.20% equity risk premium and an illustrative beta of 1.2, what required return does CAPM give?
5.29% + 1.2 x 4.20% = 5.29% + 5.04% = 10.33%. Forgetting the risk-free rate gives 5.04%; multiplying beta by the total market return double-counts the risk-free rate. CAPM covers systematic risk only.
Question 2
For Relay's integration ($150k a year for three years), discounting at 30% gives the same present value as discounting a smaller annual amount at 20%. What is that amount?
PV at 30% = 150 x 1.8161 = 272.42. At 20% the annuity factor is 2.1065, so 272.42 / 2.1065 = $129.3k. A 10-point higher rate is equivalent to a 14% haircut on the forecast, a useful way to show a board what the rate implies.
Question 3
A fund expects 70% of its investments to return 0x, 20% to return 2x and 10% to return 15x over six years. What is the expected multiple and the implied annual return?
0.2 x 2 + 0.1 x 15 = 1.9x; 1.9^(1/6) - 1 = 11.3%. A fund that needs about 11% overall must target far higher returns on each deal's success case (15x is about 57% a year), which is why venture hurdle rates exceed expected returns.
Question 4
An investment has equal chances of +40% and -20%. What is its expected return, and what does that number leave out?
0.5 x 40% + 0.5 x (-20%) = 10%. The mean says nothing about the 50% chance of a 20% loss, or whether that loss coincides with losses elsewhere in the portfolio, which is what determines the required return.
Question 5
Relay's board debates the risk that the second EHR restricts API access within a year. Where should this risk be represented?
API loss is a specific, discrete event. A higher rate penalizes distant cash flows progressively and cannot represent a cutoff. Diversified investors ignore it in the rate, but it still reduces expected cash flows, so it must be modeled there.
Question 6
A founder says, 'Our seed investors hold 40 companies, so diversification has eliminated the risk of investing in us.' What is wrong?
Spreading across companies averages out specific outcomes for the investor, while shared exposures (a funding downturn, a recession) remain. The venture's failure risk is unchanged and still reduces expected cash flows, and the founder, holding one company, bears it fully.
Workbook
Module output: A linked financial analysis, operating forecast, valuation and staged-investment decision.
Sources
Original pages and full documents are in the Library edition.