Risk and Return 61In the given example, the investor had a 3-year horizon. The holding period could be in months as well,
say, January, February, and March. The principle remains the same except that the rate of return will have to
be converted to an annual rate. Exhibit 3.3 presents the returns from all the Sensex stocks.
MEASURING PORTFOLIO RETURN
The return on a portfolio of stocks, as opposed to a single stock, could be written as:
Rp= [Dp + (V 1 – V 0 )]/V 0 (3)where
Rp= Portfolio return,
Dp= Dividend receipts,
V 1 = Value of the portfolio at the end of the period, and
V 0 = Value of the portfolio at the beginning of the period.
To illustrate, if an investor were to purchase shares of RIL, Colgate Palmolive and Hindustan Lever
Limited (HLL) @ Rs 10 lac, and sell them when the value of the portfolio is Rs 12 lac, the return on the
portfolio (ignoring dividends) would be:
(12 – 10)/10 = 20 percentThe above formulation is based on the assumption that the investor does not withdraw any portion of
initial investment or inject fresh investment during the period or dividend receipts are not reinvested. If
any of these occur, the formula may have to be modified suitably. The portfolio return in case of a multi-
period situation may be written as:
V 0 = [D 1 /(1 + r)^1 ] + [D 2 /(1 + r)^2 ] + ··· + [(DN + VN)/(1 + r)N](4)where
D 1 , D 2 , and DN are dividend receipts, and
V 0 and V 1 are portfolio values at the beginning and end of the holding period.
The rate r that equates cash inflows and cash outflows is the return on the portfolio. The concept is simi-
lar to the YTM of a bond.^1 The calculation is based on the assumption that dividend receipts are reinvested
at r percent. Although the above example considers a stock portfolio, the concept can be extended to port-
folios of other assets as well.
(^1) YTM is the yield to maturity of a bond. It is the rate that equates periodic coupon receipts and principal repayments and
the market price of the bond. YTM is explained later in the chapter on debt markets.