Correlation Coefficient

A borrower's loan agreement adjusts with the prime rate. Who sets the prime rate?

1. A.The Federal Open Market Committee, at each of its regularly scheduled meetings.Wrong. The FOMC sets a target for the federal funds rate and publishes no lending rate for bank customers.
2. B.Commercial banks, as the rate charged to their most creditworthy customers.Correct. Prime is a benchmark each bank sets for its best commercial borrowers, and it follows the Fed's policy stance.
3. C.The Board of Governors, as a ceiling on what banks are permitted to charge.Wrong. The Board sets reserve requirements and approves discount rates; it does not cap what banks may charge.
4. D.The Treasury, as part of its management of federal government borrowing costs.Wrong. The Treasury borrows money and manages federal debt, playing no part in setting bank lending rates.

Why: The prime rate is a commercial bank rate, quoted by banks for their strongest borrowers and used as a reference for many floating-rate loans. Banks move it in response to the Fed's policy stance, because the cost of the reserves funding those loans tracks the federal funds market. That relationship is why prime rises after a tightening and falls after an easing, but the decision belongs to the banks themselves. The Fed's own rates are the discount rate it charges banks and the federal funds target it steers toward.

An investor holds one stock and adds a second whose returns have historically moved almost exactly in step with the first. What is the effect on the portfolio's risk?

1. A.Risk falls sharply, because the portfolio now holds two securities rather than one.Wrong. Counting positions is not diversifying, since the benefit comes from holdings that do not move together.
2. B.Risk rises, because holding two separate positions doubles the exposure to loss.Wrong. Splitting the same money between two positions does not increase the amount at risk.
3. C.Risk is little changed, because the two move together and offset nothing.Correct. Diversification works through imperfect correlation, and there is virtually none available here.
4. D.Risk falls to the level of the market, because two holdings constitute diversification.Wrong. Reaching market-level risk requires broad exposure across many holdings that move independently.

Why: The risk reduction from diversification comes from holdings that do not move in lockstep, so that a loss in one is partly offset by the behavior of another. When two securities are almost perfectly positively correlated there is nothing to offset, and the pair behaves much like a single holding. The lower the correlation between an addition and the existing portfolio, the greater the benefit, and a negatively correlated addition helps most of all. No amount of adding, however uncorrelated, removes the market-wide component of risk.

Combining two assets provides the GREATEST diversification benefit when their returns have a correlation of:

1. A.0.0Wrong. Zero correlation helps, but negative correlation helps more.
2. B.-1.0Correct. Perfect negative correlation gives the maximum offset.
3. C.+1.0Wrong. Perfectly positive correlation provides zero diversification benefit.
4. D.+0.5Wrong. Some benefit exists, but far less than at -1.0.

Why: Portfolio risk reduction from combining assets grows as correlation decreases; at -1.0, movements offset completely, permitting maximum variance reduction. Citation: modern portfolio theory (Markowitz). Takeaway: the lower (more negative) the correlation, the better the diversification.

Two funds have a correlation coefficient of -0.2. Combining them in a portfolio will:

1. A.Have no diversification effect, because only a correlation of exactly -1.0 provides a benefitDiversification is a sliding scale. Every correlation below +1.0 produces some benefit.
2. B.Reduce portfolio risk more than combining two funds with a correlation of +0.6, because lower correlation improves diversificationCorrect. The lower the correlation, the greater the risk reduction from combining the assets.
3. C.Increase portfolio risk, because negative correlation means the funds work against each otherMoving in opposite directions smooths the combined portfolio. It is the source of the benefit, not a harm.
4. D.Eliminate portfolio risk entirely, because the correlation is negativeOnly perfect negative correlation at precise weights could theoretically eliminate risk, and -0.2 is far from that.

Why: The correlation coefficient runs from -1.0 to +1.0. Diversification benefit increases as correlation falls, so -0.2 diversifies more effectively than +0.6. But negative correlation does not eliminate risk - only a perfect -1.0 in exactly offsetting proportions could do that, and it does not occur in practice. Negative correlation means the two tend to move in opposite directions, which smooths the combined result rather than working against the investor.