There Are Two Ways To Calculate The Expected Return Of A Por

There Are Two Ways To Calculate The Expected Return Of A Portfolio Ei

There are two ways to calculate the expected return of a portfolio: either calculate the expected return using the value and dividend stream of the portfolio as a whole, or calculate the weighted average of the expected returns of the individual stocks that make up the portfolio. Which return is higher? What are the advantages and disadvantages of each? Please explain the calculations of the two ways using an example and the reasons. Thank you.

Paper For Above instruction

The expected return of a portfolio is a fundamental concept in finance, serving as a measure of the anticipated profitability based on the assets it contains. There are two primary methods for calculating this measure: the aggregate or overall portfolio approach and the weighted average of individual asset returns. Each approach offers unique insights, advantages, and limitations, and understanding their differences is essential for effective portfolio management and investment decision-making.

Method 1: Calculating Expected Return Using Portfolio Value and Dividends

The first method involves calculating the expected return based on the entire portfolio's value and its overall dividend streams. This approach considers the portfolio as a single entity, reflecting the collective performance of all holdings combined. The formula for this method is:

E(Rp) = (D + V - V0) / V0

where:

  • E(Rp) = expected return of the portfolio
  • D = expected dividends received from the portfolio
  • V0 = initial total value of the portfolio
  • V = expected value of the portfolio at the end of the period

This method simplifies the calculations by focusing on the total expected cash flows and valuation changes, effectively yielding a single aggregate return.

Method 2: Calculating the Weighted Average of Individual Returns

The second method involves calculating the expected returns of each individual stock within the portfolio and then taking a weighted average based on the proportion of each stock in the portfolio. The formula is:

E(Rp) = w1  E(R1) + w2  E(R2) + ... + wn * E(Rn)

where:

  • w1, w2, ..., wn = weights of each stock in the portfolio (proportion of total value)
  • E(R1), E(R2), ..., E(Rn) = expected returns of individual stocks

This method decomposes the portfolio return into constituent parts, reflecting the contribution of each stock based on its weight and expected return.

Example Illustration

Suppose a portfolio consists of two stocks, Stock A and Stock B. The initial investments are $6,000 in Stock A and $4,000 in Stock B, making the total initial portfolio value $10,000. The expected return of Stock A is 8%, and Stock B is 12%. The expected dividends are $200 for Stock A and $150 for Stock B, with an expected end-of-period total value of $10,600 for the portfolio.

Using Method 1:

The total expected dividends are $200 + $150 = $350. The expected portfolio value at the end is $10,600. The initial value is $10,000. Therefore:

E(Rp) = (350 + 10,600 - 10,000) / 10,000 = (950) / 10,000 = 9.5%

Using Method 2:

The weights are:

  • Weight of Stock A: wA = 6,000 / 10,000 = 0.6
  • Weight of Stock B: wB = 4,000 / 10,000 = 0.4

The expected returns are 8% and 12%, respectively. The weighted average expected return is:

E(Rp) = 0.6  8% + 0.4  12% = 4.8% + 4.8% = 9.6%

Comparing the two results: Method 1 yields an expected return of 9.5%, while Method 2 gives 9.6%. The slight difference arises from the way dividends and valuation changes are incorporated and highlights that, in practice, small discrepancies can occur due to timing, dividend treatment, or assumptions.

Discussion of Advantages and Disadvantages

Method 1 Advantages:

  • Provides a holistic view of the portfolio's expected return, incorporating total cash flow and valuation effects.
  • Simplifies calculations for portfolios where detailed asset-level data may be unavailable.

Method 1 Disadvantages:

  • Less granular; does not reveal the contribution of individual assets.
  • Depends on the accuracy of aggregate data, which can mask underlying risks.

Method 2 Advantages:

  • Offers detailed insight into the contribution of each asset, aiding in risk assessment and portfolio optimization.
  • More adaptable to dynamic adjustments and individual asset performance analysis.

Method 2 Disadvantages:

  • Requires detailed expected return estimates for each asset, which can be challenging to forecast accurately.
  • Assumes weights and returns are independent, which may not hold in volatile markets.

Conclusion

The choice between these two methods depends on the context and available information. The aggregated approach provides a straightforward, high-level estimate of expected returns, suitable for broad portfolio analysis. Conversely, the weighted average method allows for a more nuanced understanding of asset contributions, crucial for active management and risk balancing. Analysts often use both methods complementarily to gain comprehensive insights into portfolio performance estimates, thereby enhancing investment decision-making and risk management.

References

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