Lesson 2 of 7 · 11 min

Lending, borrowing and leveraged portfolios on the CML

Left of the market portfolio you lend at the risk-free rate; right of it you borrow to hold more than 100% in the market, raising both risk and expected return, and a higher borrowing rate bends the line down.

In short

  • Between RfR_f and M, investors hold positive amounts of the risk-free asset: lending portfolios.
  • Right of M, the risk-free weight is negative: the investor borrows and holds a leveraged (borrowing) position in the market.
  • The same formulas work with a negative w1w_1: E(Rp)=w1Rf+(1−w1)E(Rm)E(R_p) = w_1R_f + (1 - w_1)E(R_m) and σp=(1−w1)σm\sigma_p = (1 - w_1)\sigma_m.
  • If the investor must borrow at Rb>RfR_b > R_f, the CML is kinked at M: the borrowing segment has the lower slope [E(Rm)−Rb]/σm[E(R_m) - R_b]/\sigma_m.
  • Only less risk-averse investors choose leveraged portfolios; all passive portfolios still lie on the (possibly kinked) CML.

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Lending, borrowing and leveraged portfolios on the CML · Portfolio Risk and Return: Part II