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Read the link between risk and reward, and show how risk management can be distorted when interests conflict.

FRM® Part I · Foundations of Risk Management · The Building Blocks of Risk Management · FRM1.FR.1.d

The idea

Risk and reward are linked, because investors and firms expect higher expected returns for bearing more risk. Under the CAPM, and in a frictionless efficient-market framework generally, only systematic risk is priced, since it cannot be diversified away. Idiosyncratic risk can be diversified away and earns no premium. Performance should therefore be judged per unit of risk, for example with the Sharpe ratio, or with risk-adjusted capital measures. The measure is Sharpe ratio = (portfolio return − risk-free rate) ÷ σ. Here σ is the standard deviation of the portfolio's excess return. The link is distorted when interests conflict, which is the agency problem. A trader paid a share of profits but not charged for losses holds a payoff like a call option and gains from extra risk. Shareholders of a leveraged firm can gain at the expense of lenders by shifting to riskier assets. Risk managers who report to, or are paid by, the business they police lose independence. Remedies are independent reporting lines, deferred and clawback-able pay, and incentives tied to risk-adjusted results.

Formulas

Sharpe ratio

Sharpe ratio = (Rp − Rf) ÷ σp

Rp
the portfolio's return
Rf
the risk-free rate
σp
the standard deviation of the portfolio's return

Excess return per unit of total risk. Forgetting to subtract Rf can reverse a ranking between a low-risk and a high-risk fund.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a frictionless efficient-market framework such as the CAPM, which risk should an investor expect to be compensated for bearing?

  1. Total risk, including firm-specific risk that could be diversified.Why not: Specific risk can be diversified at low cost, so the market does not pay a premium for it.
  2. Systematic risk that cannot be diversified away. - correct
  3. Operational risk, because firms choose to accept it.Why not: Operational risk is generally not rewarded; a firm earns no return for process failures.
  4. Only risk that has already produced realized losses.Why not: Compensation depends on the exposure ex ante, not on whether a loss has happened.

Priced risk is the part investors cannot diversify. Idiosyncratic risk can be eliminated in a diversified portfolio and so earns no premium.

A harder one

Fund A earned 5% with a standard deviation of 5%. Fund B earned 8% with a standard deviation of 10%. The risk-free rate is 3%. Which statement is correct?

  1. Fund A has the higher Sharpe ratio, 1.00 against 0.80, because it earns more return per unit of risk.Why not: Divides total return by risk without subtracting the risk-free rate.
  2. Fund A is better because it has the lower standard deviation, so its Sharpe ratio must be higher.Why not: Assumes lower risk implies a higher Sharpe ratio, ignoring the return earned above the risk-free rate.
  3. Fund B is better because its 8% return is higher, and a higher return means better risk-adjusted performance.Why not: Ranks on return alone without adjusting for the risk taken.
  4. Fund B has the higher Sharpe ratio, 0.50 against 0.40. - correct

Sharpe = (return - risk-free) / standard deviation: A = (5 - 3) / 5 = 0.40 and B = (8 - 3) / 10 = 0.50. Ignoring the risk-free rate would wrongly favour A.

The hardest tier

At a trading firm the head of risk reports to the head of trading, and the risk team's bonus pool depends on desk profits. Traders repeatedly breach limits with little consequence. Which change best addresses the root cause?

  1. Raise the VaR limits so that fewer breaches are recorded.Why not: Treats the symptom cosmetically; the conflict between control and revenue remains.
  2. Make risk independent: report to the CEO and board risk committee, with pay not linked to desk profit. - correct
  3. Increase the traders' share of profits so they bear more of the upside and align with shareholders over the long run.Why not: A larger share of upside without a share of losses strengthens the incentive to take risk.
  4. Require traders to certify their own positions each day.Why not: Relies on the conflicted party to police itself and does not restore the independence of the control function.

The root cause is a conflict of interest: the people who control risk are dependent on the business they control. Independent reporting and pay not tied to desk revenue restore the control function's authority.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

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