Download expected rate of return

Study unit 4
RISK AND RETURN SUMMARY
ASSET’S RATE OF RETURN
𝒓𝒕 =
𝒓𝒕
𝑪𝒕
𝑷𝒕
𝑷𝒕−𝟏
Where
𝑪𝒕 + 𝑷𝒕 − 𝑷𝒕−𝟏
𝑷𝒕−𝟏
= actual, expected, or required rate of return during period t
= cash (flow) received from the asset
= new price
= old price
HOLDING PERIOD RETURN
The formula used is similar to the one for asset rate of return
𝑯𝑷𝑹 =
𝑫
𝑪𝒕
𝑷𝒕
𝑷𝒕−𝟏
Where
𝑫 + 𝑷𝒕 − 𝑷𝒕−𝟏
𝑷𝒕−𝟏
= actual, expected, or required rate of return during period t
= cash (flow) received from the asset
= new price
= old price
EXPECTED RATE OF RETURN
The expected rate of return is the most likely return on an asset.
Use table e.g.
𝑷𝒕
0,25
0,50
0,25
Rate of
return
20%
15%
10%
𝒓 × 𝑷𝒕
0,05
0,075
0,025
𝒓̅ = 𝟏𝟓%
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STANDARD DEVIATION
Use table e.g.
𝑷𝒕
.40
.50
.10
Rate of
return
25%
10%
-10%
𝒓 × 𝑷𝒕
𝒓 − 𝒓̅
(𝒓 − 𝒓̅)𝟐
(𝒓 − 𝒓̅)𝟐 × 𝑷𝒕
10
5
-1
11
-4
- 24
121
16
576
48,4
8
57,6
Ơ𝟐 = 𝟏𝟏𝟒
𝒓̅ = 𝟏𝟒%
Ơ = √𝟏𝟏𝟒
Ơ = 𝟏𝟎, 𝟔𝟕
COEFFICIENT OF VARIATION
𝑪𝑽 =
𝝈𝒌
𝒓̅
The higher the riskier
PORTFOLIO RETURN
𝒏
𝒓 𝒑 = ∑ 𝒘𝒋 × 𝒓 𝒋
𝒋=𝟏
𝒓𝒋 = Expected return on each individual asset
𝒘𝒋 = Fraction for each respective asset investment
𝒓𝒋 = Number of assets in the portfolio
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CAPITAL ASSET PRICING MODEL (CAPM)
Expected return
𝒓𝒋 = 𝑹𝑭 + 𝒃(𝒓𝒎 − 𝑹𝑭 )
Where 𝒓 = required return on asset j
𝑹𝑭 = risk-free rate of return, commonly measured by the return on a Treasury bill
𝒃𝒋 = beta coefficient or index of non-diversifiable risk for asset j
𝒓𝒎 = market return; return on the market portfolio of assets
Risk-free rate
𝑹𝑭 =
𝒓𝒋 − 𝒃. 𝒓𝒎
𝟏−𝒃
Market return
Easy to convert just substitute the values in the expected return formula and solve for 𝒓𝒎
𝒓𝒋 = 𝑹𝑭 + 𝒃(𝒓𝒎 − 𝑹𝑭 )
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