Borrowing (leveraged) portfolio

The Capital Market Line shows every combination of the risk-free asset and the market portfolio M that a rational investor can choose. Most of that line comes from lending: putting some money in the risk-free asset and the rest in M.

But an investor is not limited to their own wealth. They can borrow at the risk-free rate, add the borrowed money to what they already have, and put the entire, enlarged amount into the market portfolio. That is a borrowing, or leveraged, portfolio. It earns the market portfolio's return on every rupee invested — including the borrowed rupees — while paying only the risk-free rate on what was borrowed. The gap between the two is pure gain to the investor, which is exactly why leverage can push the return above what the market portfolio delivers on its own.

Section 16.5 extends the CML past the market portfolio M. All combinations that only lend at the risk-free rate sit to the left of M on the line. An investor who instead borrows at the risk-free rate and invests the total in M sits to the right of M — a higher expected return, at higher risk, than M itself.

The workbook's own worked numbers: market portfolio return 20%, risk-free rate 5%.

• 100% in M, 0% in the risk-free asset: (1 × 20%) + (0 × 5%) = 20% — the maximum return possible without borrowing.
• 50% in M, 50% lent at the risk-free rate: (0.5 × 20%) + (0.5 × 5%) = 12.5%.
• Borrowing 50% of wealth and investing 150% of wealth in M: (1.5 × 20%) − (0.5 × 5%) = 27.5% — the debt component is subtracted, because the borrowed 50% is a repayment obligation to the investor, not a receipt.

Because M is the tangency point and includes every risky asset — equities, corporate bonds, commodities, gold, real estate and more — a leveraged portfolio does not change what is held; it only changes how much of M is held relative to the investor's own capital.

Illustrative figures, following the workbook's method. Mr Talwar has Rs 40,00,000 of his own money. The market portfolio M is expected to return 18% a year; he can borrow at the risk-free rate of 6%.

He borrows a further Rs 20,00,000 and invests the full Rs 60,00,000 (1.5× his own wealth) in M.

Expected portfolio return = (1.5 × 18%) − (0.5 × 6%) = 27% − 3% = 24%.

In rupee terms: Rs 60,00,000 grown at 18% = Rs 70,80,000 after one year. He owes Rs 20,00,000 × 1.06 = Rs 21,20,000 on the loan. Net wealth = Rs 70,80,000 − Rs 21,20,000 = Rs 49,60,000 — a 24% gain on his original Rs 40,00,000, exactly matching the CML formula, and higher than the 18% he would have earned by investing only his own money in M.

Had the market instead fallen 10%, the same leverage would have turned a −10% market year into a much worse loss for him, because the Rs 20,00,000 loan and its interest still have to be repaid regardless of how M performs.

Chapter 16 (Introduction to Capital Market Theory), section 16.5 (Extending the CML), gives the 20%/5% worked example with the 100%, 50% and 150%-in-M scenarios. Expect a question computing portfolio return for a stated borrowing proportion, and a conceptual one on which side of M a leveraged portfolio plots.

• The debt component is subtracted in the formula, because it is money owed, not money received — a common sign error is adding it.
• Borrowing at the risk-free rate is a simplifying assumption. In practice an investor's actual borrowing rate is higher than the risk-free rate, which the workbook flags without abandoning the model.
• A leveraged portfolio still holds only M — leverage changes the scale of exposure to the market portfolio, not its composition.
• Higher expected return from leverage comes with higher risk, in direct proportion to the leverage ratio (1.5× wealth invested means 1.5× the market portfolio's risk, roughly).
• Do not confuse this with alpha-beta separation, where a short position specifically cancels market exposure — a leveraged portfolio does the opposite, amplifying market exposure.