 # CFAI Reading 30 - Problem 29

The solution states that the return on equity (2million) is 0.5% however, that is the return on the entire portfolio of 5million. According to the formula in the text, the return on equity is supposed ot be: Return on funds invested (equity) = rf + b/e (rf-k) which comes out to 0.675% which is the return on equity. However the solution states 0.675% is the portfolio rate of return! Is this just a wording issue? Portfolio (5million) rate of return is provided in the problem which is 0.5%.

Hi, inbead. I think you are asking about Problem 29B. From my understanding of the problem and the Reading, there is a distinction between “return on equity” and return on the entire portfolio. The “return on equity”, in the context in the whole of Problem 2,9 means the return on the equity component of the \$5 million bond portfolio (which as you correctly stated is \$2 million, since the remaining \$3 million is financed with a repurchase agreement). The return on the “equity” component is given as 0.5%. When you add the dollar return on the equity component to the dollar return on the financed component and divide by \$2 million, you get 0.675% (which is the return on the entire portfolio). In the context of this problem, I would interpret the phrase “return on equity” to mean the return on the equity component of the portfolio, i.e., the \$2 million portion of the bond portfolio that is not financed with the repurchase agreement. Notice that there is no stock (i.e, equity) in the portfolio. The phrase equity, in this problem, just means the portion of the bond portfolio for which you do not need financing. Thus, \$5 million (all bonds) = \$3 million (bonds purchased using repo agreement financing) + \$2 million (bonds purchased without need of financing). Did I answer your question? I had to work a bit to understand your question.

Thanks, yes I was asking about 29B. I think i misinterpreted the question and assumed .5% was the return on the entire investment of 5mm and not the equity part. The above makes it clear.