Risk Free Borrowing and Lending

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 RISK-FREE BORROWING AND LENDING:

Assume that the efficient frontier, as shown by the arc AB in Figure 9-1, has been derived by an investor. The arc AB delineates the efficient set of portfolios of risky assets as explained in (For simplicity, assume these are portfolios of common stocks.) We now introduce a risk-free asset with return RF and σ = 0.


As shown in Figure 9-1, the return on the risk-free asset (RF) will plot on the vertical axis because the risk is zero. Investors can combine this riskless asset with the efficient set of portfolios on the efficient frontier. By drawing a line between RF and various risky portfolios on the efficient frontier, we can examine combinations of risk-return possibilities that did not exist previously.

Lending Possibilities:

 In Figure 9-1 a new line could be drawn between RF and the Markowitz efficient frontier above point X, for example, connecting RF to point V. Each successively higher line will dominate the preceding set of portfolios. This process ends when a line is drawn tangent to the efficient set of risky portfolios, given a vertical intercept of RF. In Figure 9-1, we call this tangency point M. The set of portfolio opportunities on this line (RF to M) dominates all portfolios below it. 

The straight line from RF to the efficient frontier at point M, RF-M, dominates all straight lines below it and contains the superior lending portfolios given the Markowitz efficient set depicted in Figure 9-1. Lending refers to the purchase of a riskless asset such as Treasury bills, because by making such a purchase, the investor is lending money to the issuer of the securities, the U.S. government. We can think of this risk-free lending simply as risk-free investing.

Borrowing Possibilities:

 What if we extend this analysis to allow investors to borrow money? The investor is no longer restricted to his or her wealth when investing in risky assets. Technically, we are short-selling the riskless asset. One way to accomplish this borrowing is to buy stocks on margin, which has a current initial margin requirement of 50 percent. We will assume that investors can also borrow at the risk-free rate RF.3 This assumption can be removed without changing the basic arguments. 

Borrowing additional:

Borrowing Additional investable funds and investing them together with the investor’s own wealth allows investors to seek higher expected returns while assuming greater risk. 



These borrowed funds can be used to leverage the portfolio position beyond point M, the point of tangency between the straight line emanating from RF and the efficient frontier AB. As in the lending discussion, point M represents 100 percent of an investor’s wealth in the risky asset portfolio M. The straight line RF-M is now extended upward, as shown in Figure 9-2, and can be designated RF-M-L.

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