Learn alpha and benchmark comparison — Hinglish notes

5.5.10 · Stock-Market › Portfolio Theory

BENCHMARK kya hota hai?

WHY hume benchmark chahiye: Absolute returns do chizein chhupaate hain — (1) risk-free return jo tumhe sirf paisa lend karne par milti hai, aur (2) market return jo tumhe sirf invested rehne par milti hai. Skill woh hai jo baad mein bachti hai.

ALPHA kaise define hota hai — CAPM se derive karo

Hum alpha ko first principles se banate hain using the Capital Asset Pricing Model (CAPM), jo market risk ki ek given amount ke liye fair expected return predict karta hai.

Step 1 — Building blocks.

$R_{f}$ = risk-free rate (bina risk ke return, jaise T-bills).
$R_{m}$ = market/benchmark ki return.
$R_{p}$ = tumhare portfolio ki return.
$β$ = market moves ke liye tumhare portfolio ki sensitivity.

Step 2 — Excess returns. Hume sirf risk-free rate se upar ki return ki chinta hai, kyunki $R_{f}$ sabke liye free hai. Excess returns define karo: $R_{p} - R_{f} (your reward for risk), R_{m} - R_{f} (market risk premium)$

Yeh step kyun? $R_{f}$ subtract karne se "free" baseline hatt jaata hai, isliye hum sirf risky parts ko compare karte hain.

Step 3 — CAPM ki fair prediction. CAPM kehta hai ki tumhari expected excess return exactly $β$ times market ki excess return honi chahiye: $E [R_{p} - R_{f}] = β (R_{m} - R_{f})$

Yeh step kyun? Agar tumhara portfolio market se 1.5× zyada swing karta hai ( $β = 1.5$ ), toh tumhe 1.5× risk premium milna chahiye — na zyada, na kam. Yeh us risk ki fair price hai jo tumne li.

Step 4 — Alpha shortfall ya surplus hai. Jo bhi return tumhe CAPM ki fair prediction se aage mili woh skill hai (ya luck). Rearrange karne par:

$β$ term kyun matter karta hai: Ek naive comparison hai $R_{p} - R_{m}$ (raw outperformance). Lekin agar tumne market ko beat karne ke liye zyada risk liya ( $β > 1$ ), toh woh extra return kharida gaya tha, kamaya nahi. Alpha exactly iske liye correct karta hai market premium ko $β$ se scale karke.

Figure — Learn alpha and benchmark comparison

Upar ka chart Security Market Line (SML) hai: CAPM ki fair line. Line ke upar ke points ka alpha positive hai (vertical distance = $α$ ); line ke neeche waalon ka alpha negative hai.

WHY alpha ≠ raw outperformance

Worked examples

Common mistakes

Forecast-then-verify

Flashcards

Benchmark kya hota hai?

Ek reference portfolio (jaise ek index) jo performance ko ek default investable alternative ke relative judge karne ke liye use hota hai.

Jensen's alpha ko ek formula mein define karo.

α = (R_{p} - R_{f}) - β (R_{m} - R_{f})

R_{p} - R_{m}

skill ka acha measure kyun nahi hai?

Yeh risk ignore karta hai — higher

β

(leverage) se extra return free hai, skill nahi.

β (R_{m} - R_{f})

kya represent karta hai?

Woh fair excess return jo CAPM kehta hai ki tumhe tumhare liye gayi market risk ke liye milni chahiye.

Ek fund market ko 5% se beat karta hai lekin

β = 2

hai aur

R_{m} - R_{f} = 5%

. Alpha?

Fair excess =

2 \times 5 = 10%

; raw excess =

5 + 5 = 10%

⇒

α = 0

. No skill.

Security Market Line par positive alpha kaisa dikhta hai?

Portfolio point SML ke upar plot hota hai; alpha vertical distance hai.

Kya index se peeche rehne wala fund phir bhi positive alpha rakh sakta hai?

Haan — agar uska

β

low hai aur usne apni (chhoti) fair return beat ki, jaise ek defensive fund.

β = 0

market-neutral fund ka alpha kya hota hai?

R_{f}

ke upar uski poori excess return, kyunki woh koi market risk nahi uthata.

Recall Feynman: explain to a 12-year-old

Ek race imagine karo jahan sabko ek moving walkway milta hai jo unhe aage le jaata hai for free (woh market hai). Agar tum aage finish karo, yeh impressive nahi hai agar walkway ne kaam kiya. Alpha woh hai ki tum kahan finish karte jahan sirf walkway tumhe le jaata uss se kitna aage ho. Agar tum tez walkway par daud rahe the (zyada risk), toh hum expect karte hain tum zyada aage hoge — isliye doosron ko beat karna kaafi nahi; tumhe woh beat karna hoga jo tumhara walkway tumhe dena chahiye tha.

Connections

Capital Asset Pricing Model (CAPM) — woh fair-return prediction provide karta hai jiske against alpha measure hota hai.
Beta and Systematic Risk — woh $β$ term jo market premium ko scale karta hai.
Security Market Line — visual line; alpha = isse vertical distance.
Sharpe Ratio — alternative risk-adjusted measure jo $β$ ki jagah total risk (σ) use karta hai.
Risk-free Rate — woh baseline jo excess returns compute karne se pehle subtract hoti hai.
Efficient Market Hypothesis — yeh claim ki consistent positive alpha kamaana bahut mushkil hai.