These questions follow the quantitative core of the CFA Level 1 curriculum, covering time value of money, fixed income, derivatives, economics and portfolio management. Each answer works through the reasoning rather than just stating the result.
Try to answer each one aloud before reading the solution, the way an interviewer would ask it.
Future value equals present value times (1 plus r) to the power n, so $1,000 x 1.06 to the power 10, which is approximately $1,791. The $791 of growth is not simply 6% x 10 years x $1,000, which would be $600. The extra $191 is interest earned on previously accumulated interest, which is compounding. The gap widens sharply with time and rate, and understanding that difference between simple and compound growth underpins the entire time value of money topic.
72 divided by 9 equals 8 years. The exact answer, from taking the log of 2 divided by the log of 1.09, is 8.04 years, so the approximation is excellent here. The rule is most accurate between roughly 6% and 12% and drifts at the extremes. It can be inverted too: to double in five years you need approximately 72 divided by 5, or about 14.4% annually.
The Sharpe ratio equals the portfolio return less the risk free rate, divided by the portfolio's standard deviation. It measures excess return earned per unit of total risk. A portfolio returning 12% with 15% volatility against a 3% risk free rate has a Sharpe of 0.6. It allows comparison between portfolios with different risk levels, since raw return alone tells you nothing about the risk taken to achieve it. The main limitation is that standard deviation penalises upside and downside volatility equally, which is why the Sortino ratio, using downside deviation only, is sometimes preferred.
Apply CAPM: required return equals the risk free rate plus beta times the equity risk premium, so 3% plus 1.4 x 5%, which equals 10%. Beta of 1.4 means the stock has historically moved about 1.4 times as much as the market, so it carries more systematic risk and investors demand more return. CAPM prices only systematic risk, on the reasoning that company specific risk can be diversified away and therefore earns no premium.
A bond's coupon is fixed at issue. If market yields rise, new bonds pay more, so an existing bond's fixed payments are worth less by comparison and its price must fall until its yield to maturity matches the market. In present value terms, price is the discounted value of fixed future cash flows, so a higher discount rate produces a lower price. The relationship is also convex rather than linear: prices rise more when yields fall than they fall when yields rise by the same amount.
Modified duration estimates the percentage price change of a bond for a 100 basis point change in yield. A duration of 7 implies roughly a 7% price fall if yields rise one point. PVBP, the price value of a basis point, is the currency change in price for a one basis point move, calculated as modified duration x price x 0.0001. Duration rises with longer maturity and falls with a higher coupon, because a larger coupon returns cash sooner and shortens the weighted average time to receipt.
No-arbitrage requires that investing for two years at the two year spot equals investing one year at the one year spot and reinvesting at the forward rate. So (1.04) squared equals (1.03) x (1 plus f). That gives 1.0816 divided by 1.03, which is 1.0501, so the forward rate is approximately 5.01%. The forward rate exceeds both spot rates because an upward sloping curve requires the later period to carry a higher rate to pull the average up.
The quick approximation subtracts: 7% less 4% equals 3%. The exact Fisher relationship is (1 plus nominal) divided by (1 plus inflation), less 1, giving 1.07 divided by 1.04 less 1, which is 2.88%. The approximation is adequate at low rates but degrades badly at high inflation. At 50% nominal and 40% inflation, subtraction suggests 10% while the exact calculation gives 7.1%. Real return is what actually matters, since it measures purchasing power gained.
For European options on a non-dividend paying stock: call price plus the present value of the strike equals put price plus the spot price. Holding a call and enough cash to exercise gives the same payoff at expiry as holding a put and the stock itself, so the two must cost the same today or a riskless arbitrage exists. It is the reason a call and put with the same strike and expiry cannot be priced independently, and it lets you derive any one of the four inputs from the other three.
Combining assets that are not perfectly correlated means their individual movements partially offset, so portfolio standard deviation falls below the weighted average of the individual deviations. The lower the correlation the larger the benefit, and with correlation below 1 some risk always cancels. The limit is systematic risk: factors such as interest rates, recessions and broad market moves affect nearly all assets together and cannot be diversified away. This is why CAPM rewards only systematic risk, since unsystematic risk can be eliminated for free.
Time-weighted return removes the effect of cash flows into and out of the portfolio by chaining sub-period returns, so it measures the manager's performance irrespective of client timing. Money-weighted return is effectively the IRR of the portfolio and does reflect the size and timing of contributions, so it measures the investor's actual experience. Time-weighted is the standard for comparing managers and is required under GIPS. Money-weighted is more informative when the decision maker controls the cash flow timing, as in private equity.
Discount each inflow: $60 divided by 1.10 equals $54.55, and $60 divided by 1.21 equals $49.59. The sum is $104.14, and subtracting the $100 outlay gives an NPV of approximately +$4.13. The NPV is positive so the project earns more than the 10% required return and should be accepted. The IRR here is roughly 13.1%, which is the rate at which NPV would equal zero, and consistently exceeds the 10% hurdle.
Every concept above maps to a module you can practise, with the numbers regenerating on each attempt.
Reading an answer once is recognition. Interviews test recall under pressure, so the questions regenerate with fresh numbers every run.
Start practising freeNo. They are original practice questions written in the style of the Level 1 curriculum, covering the same quantitative concepts. MDPrep is not affiliated with or endorsed by the CFA Institute, and CFA is a trademark owned by the CFA Institute.
The quantitative core: quantitative methods, economics, corporate issuers, equity valuation, fixed income, derivatives, alternatives and portfolio management. Ethics and professional standards are a substantial part of the real exam but are not covered here, since the app focuses on calculation and applied reasoning.
On its own, no. Level 1 demands broad curriculum coverage including ethics and financial reporting detail. Practice of this kind is best used to make the quantitative material automatic, so that exam time can be spent on reasoning rather than on recalling mechanics.